KAYATTA, Circuit Judge.
These consolidated appeals present a rare example of a trial record that lacks sufficient evidence to support a guilty verdict returned by a jury. Carlos López-Díaz (“Carlos”), a dentist, operated a mobile dental clinic in Puerto Rico.1 His brother, José López-Díaz (“José”), is a medical doctor who billed Medicare for services to Carlos’s patients that José never provided. The jury convicted José of health-care fraud, conspiracy to commit [109]*109health-care fraud, and aggravated identity-theft for using personal information gathered from Carlos’s patients. Based on the fact that Carlos gave José access to his patient billing information while knowing that José never treated, or even saw, any of the patients, the government also obtained a verdict against Carlos on the conspiracy and aggravated identity theft charges. While we find no error in José’s convictions, we reverse the verdict against Carlos because the prosecution did not present enough evidence to support his convictions without undue speculation.
I. Background
We limit our summary here to the basic contours of the health-care fraud scheme and proceedings below, reserving a fuller exposition of the relevant facts in the proper light for our discussion of particular issues. See United States v. Flores-Rivera, 787 F.3d 1, 9 (1st Cir.2015).
Between January 2006 and July 2011, José submitted 10,231 claims for reimbursement to Medicare, totaling approximately $3,500,000, of which Medicare actually paid about $700,000. He submitted the claims using Health Insurance Claim Form 1500 (“CMS 1500 Form”), a form used for Medicare billing by Centers for Medicare and Medicaid Services (“CMS”), which administers the Medicare program. As it turns out, José never provided any of the medical procedures for which he sought reimbursement. In some instances, he claimed to have provided services to Medicare beneficiaries who were deceased. He also repeatedly billed for the same unusual procedures. José filed 1,177 claims (far more than anyone else in Puer-to Rico) for a procedure typically performed by urologists, and more than half of those claimed urological procedures were for female patients, even though the procedure can be performed on male patients only.
In order to submit those false claims, José needed the Medicare beneficiaries’ identifying and health coverage information. His principal sources were the patient records of his brother Carlos, a licensed dentist. Beginning sometime in 2007, Carlos operated a mobile dental clinic — essentially, a large trailer with three dental chairs and necessary equipment— to provide dental services to underserved patients at nursing homes, mental health residential facilities, and schools. Carlos employed a coordinator to visit potential facilities, market the clinic, schedule visits, and collect patient medical histories, consent and release forms, and health coverage information before the mobile clinic visited each facility. Carlos also employed two dental assistants.
José never treated or even saw any of Carlos’s patients. Rather, José testified that Carlos gave him access to dental patient information as part of a safety protocol developed by the brothers after one of Carlos’s elderly patients suffered a heart attack or stroke in the mobile clinic in late 2007, an event confirmed by the director of the stricken patient’s nursing home. Two of the witnesses called by the government, Leslie Williams-Nieves (“Williams”) and Nahír Rodríguez-Candelario (“Rodrí-guez”), explained that they were told that a regulation enacted by the Puerto Rico State Department required Carlos to have his patients medically evaluated and to use a medical consultant. When asked about this regulation, José said that he could not recall its name.2 Pursuant to the protocol, José paid Carlos’s dental assistants to take and record vital signs of dental patients [110]*110before Carlos treated them, with José available for phone consultations, and José would later review the patient files, vital signs, and medical histories to see that Carlos’s staff was acting properly.3 The parties agree that José did indeed pay the dental assistants to take and record patient vital signs, and the actual patient records show that José did review, or at least initial, that information in each record. According to José’s testimony, “[t]here are several formulas through which the physician can be paid for these services.”
José also gathered from Carlos’s patiént records the personal identifying information needed to bill Medicare. José used that information to complete and submit CMS 1500 Forms for medical procedures that he never performed on those patients. José paid Williams4 and Rodriguez,5 employees of his wife’s pediatric clinic, to complete his CMS 1500 Forms using information gleaned from Carlos’s patient files. Williams and Rodriguez also did separate billing and data entry work part-time for Carlos. Williams and Rodriguez testified that they filled out José’s CMS 1500 Forms either at their own homes or at José’s home office, and never in Carlos’s presence or at his office. The government stipulated that Carlos did not sign or prepare any of José’s CMS 1500 Forms, and that Carlos’s name did not appear on those forms.
Investigators eventually caught on to José’s falsified bills, and a grand jury indicted José, Carlos, Williams, Rodriguez, and others for conspiracy to commit health-care fraud in violation of 18 U.S.C. § 1849 (count one) and health-care fraud in violation of 18 U.S.C. § 1347 (counts ten through thirty), and José and Carlos for aggravated identity theft in violation of 18 U.S.C. § 1028A(a)(l) (counts thirty-one through thirty-five). All of the defendants except for Carlos were also indicted for additional counts of health-care fraud (counts two through nine).6 After a fifteen-day trial, the jury convicted José of all counts.7 The jury also convicted Carlos of the conspiracy and aggravated identity theft counts, but acquitted him of the substantive health-care fraud counts. The district court sentenced José to a total of 121 months in prison. Carlos received a total prison sentence of thirty-six months and a day. Carlos and José timely filed separate appeals challenging their convictions.8
[111]*111II. Carlos’s Insufficiency of the Evidence Claim
We turn first to Carlos’s appeal from the order denying his motion -for acquittal based on insufficient evidence to convict. See Fed.R.Crim.P. 29. We review de novo the denial of a Rule 29 motion for acquittal, asking whether a reasonable jury could find guilt beyond a reasonable doubt. United States v. Burgos-Montes, 786 F.3d 92, 112 (1st Cir.2015). In assessing a challenge to the sufficiency of the evidence, we “examine the evidence, together with all inferences that may be reasonably drawn from it, in the light most favorable to the prosecution.” United States v. Andújar, 49 F.3d 16, 20 (1st Cir.1995). Where, as here, “a jury draws inferences from circumstantial evidence, a reviewing court should refrain from second-guessing the ensuing conclusions as long as (1) the inferences derive support from a plausible rendition of the record, and (2) the conclusions flow rationally from those inferences.” United States v. Spinney, 65 F.3d 231, 234 (1st Cir.1995). Our deference to jury verdicts is not without limit, however: “[I]f the evidence viewed in the light most favorable to the verdict gives equal or nearly equal circumstantial support to a theory of guilt and a theory of innocence of the crime charged, this court must reverse the conviction,” because in such a case “a reasonable jury must necessarily entertain a reasonable doubt.” United States v. Flores-Rivera, 56 F.3d 319, 323 (1st Cir.1995) (internal quotation marks and emphasis omitted).
The parties agree that the conspiracy charge9 against Carlos turns largely on whether the jury could reasonably find that Carlos “knew” that his brother was defrauding Medicare. The parties likewise agree that the aggravated identity theft counts required the jury to find that Carlos, either as a principal or aider and abettor, “knew” of the underlying health-care fraud.10 Such knowledge for either offense could be proven by knowledge in fact, or by proof of “willful blindness.” To establish willful blindness, the government had to show that-Carlos (1) “was aware of a high probability of wrongdoing,” and (2) “consciously and deliberately avoided learning of the wrongdoing.” United States v. Appolon, 695 F.3d 44, 57 (1st Cir.2012).
The government did manage to prove that Carlos knew that José gathered from the files of Carlos’s patients information to be used by José to bill Medicare for some[112]*112thing. In its brief and at argument, the government also claimed that the evidence showed that Carlos paid his employees to complete the CMS 1500 Forms used by José to bill Medipare. Apparently accepting the government’s view of- its proof in denying Carlos’s motion to acquit, the district court expressly pointed to such payments by Carlos. See United States v. López-Díaz, 940 F.Supp.2d 39, 64 (D.P.R.2013) (“[Carlos] even paid his employees for filling out billing forms when [José] was unable to pay them.”). As the government clarified after oral argument, however, the record shows only that Carlos paid his employees to record his patients’ vital signs for José’s review, and only when José was unavailable to make this payment himself.11 Further, the government points us to no evidence that José needed (or even used) the vital signs data to deceive Medicare.
Of course, if Carlos knew that José had no basis whatsoever to bill Medicare for any amount in connection with Carlos’s patients, then his knowledge that José was billing for something could suffice to sustain the verdict. So the question is posed: Did Carlos know that José could not bill merely for the gathering and review of vital signs information? On this crucial point, the record is a complete blank. The record does not even show that such a file review is not billable, much less that Carlos knew it was not billable. The government did not submit any evidence challenging the existence of the regulation that its own witnesses cited as a reason for taking the vital signs and reviewing them. Nor did it seek an instruction on the regulation. The government also failed to counter José’s testimony that “[t]here are several formulas through which the physician can be paid” for services to mobile dental clinics. Instead, the government simply argued in closing that José did not bill for reviewing the vital signs. This was a compelling point against -José, but carried weight against Carlos only if there was evidence that Carlos knew what José was billing for.
In an effort to fill this gap, the government in its brief tells us that Carlos “is also a medical provider, submits dental billing claims himself, and understands what is required of medical provider [sic] in order to submit claims.” Cf. United States v. Singh, 390 F.3d 168, 188 (2d Cir.2004) (jury could, infer that physician/clinic owner was aware that claims he submitted were false, based on his possession of and familiarity with the applicable billing code guidebook and manual, and discussions with employees revealed his “detailed knowledge” about billing). The government, however, cites no evidence to support this crucial assertion, nor can we find any. To the contrary, the record shows that the dental billing codes (with which one could assume Carlos was familiar) were so different from the physician billing codes that the government’s own witness on Medicare billing professed almost complete ignorance about dental billing codes.12
Our own review of the record points to no other means to close this gap. Notwithstanding the indictment’s express charge that the aim of the conspiracy was to enrich both José and Carlos, there is no [113]*113evidence at all that Carlos received even one penny of the fraudulent proceeds. What little else we could find on our own review of the record added nothing to the government’s case; rather, it helped Carlos.13 We also do not think that whether and when file reviews are billable to Medicare are matters of common knowledge that lay jurors might bring to bear to connect the too-widely spaced dots in the government’s case.
José’s behavior as described by the government’s evidence offered no hint that Carlos was aware of the nature of José’s billing. The fact that José indisputably initialed the patient files suggests strongly that he was trying to deceive someone other than Medicare (e.g., Carlos?), given that the vital signs data from Carlos’s patients provided no information that José used to bill or to justify billing for the surgical and other procedures he claimed to have performed. José was also careful that Williams and Rodriguez, his wife’s employees whom he paid to fill out the demographic and health plan sections of his CMS 1500 Forms, performed their task out of Carlos’s presence. Neither did those two employees suggest that Carlos knew the services for which José was billing.
Though not clear from its brief, the government appears to argue that the jury could 'infer Carlos’s knowledge of José’s fraud if the jury doubted the utility of the treatment protocol, and thus the plausibility of Carlos’s explanation for handing his files to José. If the evidence allowed the jury to conclude that the treatment protocol was obviously useless, then the jury might have inferred that Carlos could not possibly have thought the protocol valuable. And from that the jury could, perhaps, have further inferred that Carlos must have had some other, criminal, reason for handing over his patient files to José, and thus still further inferred that Carlos must have had the requisite knowledge of José’s fraud.
The government, though, did not present any evidence to support such a chain of inferences. Acting almost as if it bore no burden of proof in making its case against Carlos, the government did not present any direct evidence that the protocol was, in fact, not an accepted or recognized method of ensuring that the mobile clinic’s practice was adhering to medical standards.14 Nor did the government present any direct evidence that Carlos believed [114]*114the protocol was useless. And, indeed, the fact that Carlos supervised his dental assistants in taking vital signs — and paid them for doing so when José was out of town — would seem to suggest that Carlos viewed the protocol as beneficial. As a result, the record cannot support the first link in a chain of inferences that would be needed to justify the jury’s verdict against Carlos on these grounds. See United States v. Burgos, 703 F.3d 1, 10 (1st Cir.2012) (“[W]e are loath to stack inference upon inference in order to uphold the jury’s verdict.” (quoting United States v. Valerio, 48 F.3d 58, 64 (1st Cir.1995))).
Our respect for a jury’s ability to get it right does nevertheless cause us to pause cautiously before concluding that the evidence is insufficient to support the verdict. We note, though, that the prosecutor in closing told the jury that “it doesn’t matter for purposes of this case if [Carlos] knew what [José] was writing on those [CMS 1500 forms]. It doesn’t make a difference.” The prosecutor also seems to have slipped into an argument based on a lesser negligence standard, rather than knowledge or willful blindness: “[Carlos], as a dentist, should have known better, or should have known better to question himself — or his brother in this case — what he was billing for if he — once he knew he wasn’t even seeing his patients.” While we have not been asked to vacate the verdict because of these statements, and while the statements might be read in context in a manner that would render them proper, they do explain how a jury could mistakenly convict Carlos in light of the absence of any evidence that his brother could not bill Medicare at all for his work under the protocol, or that Carlos knew of or willfully ignored such a limitation. We have in mind, too, the fact that in a three-week trial focused mostly on José, both the prosecutor and the trial judge themselves mistakenly thought that Carlos paid to have some of José’s falsified claim forms completed.15 In any event, the key point now is that the record contains insufficient evidence to support a reasonable inference that, beyond a reasonable doubt, Carlos knew that José had no basis for submitting any type of claim in connection with his review of Carlos’s patient records.
We therefore vacate Carlos’s convictions and remand for a judgment of acquittal of Carlos on all counts.16
III. José’s Claims
José does not challenge on appeal the sufficiency of the evidence against him on any of the counts. Rather, he points to what he claims are errors in the indict-ment, the review of alleged Brady material, and the jury instructions. We address these claimed errors in turn.
A. The Sufficiency of the Indictment’s Aggravated Identity Theft Counts
José first argues that the aggravated identity theft counts (counts thirty-one through thirty-five) of the superseding indictment were defective for lack of a corresponding substantive health-care fraud count. The aggravated identity theft counts of the indictment alleged that José knowingly possessed, transferred, or used the identification of another person without lawful authority “in relation to felony violations enumerated in subsection (c) [of 18 U.S.C. § 1028A] as: (1) Healthcare Fraud, a violation of [18 U.S.C. § 1347], [115]*115not charged herein.” • Each count listed a specific individual whose identity was used to commit the offense. The indictment did not include separate section 1347 healthcare fraud charges with' respect to the individuals named in the aggravated identity theft counts. According to José, because the government did not separately charge and convict him of the predicate health-care fraud crimes underlying the aggravated identity theft charges, the indictment was defective.17
The predicate felony violation in section 1028A is simply an element of the crime of aggravated identity theft. The statute requires proof beyond a reasonable doubt of a felony violation, not a felony conviction. It therefore did not require the government to charge José separately with the predicate healthcare fraud offenses. See United States v. Stepanian, 570 F.3d 51, 59-60 & n. 15 (1st Cir.2009) (“To the extent [the defendant] wishes to argue that the government must separately allege and charge the predicate crime in order to charge a § 1028A offense ... the statutory language lends no support to that proposition.”); see also United States v. Jenkins-Watts, 574 F.3d 950, 970 (8th Cir.2009). Moreover, the indictment adequately informed José that the predicate offenses for the aggravated identity theft counts were health-care fraud crimes “not charged herein.” See United States v. Savarese, 686 F.3d 1, 6 (1st Cir.2012) (“[A]n indictment is adequate if it specifies the elements of the offense charged, fairly apprises the defendant of the charge against which he must defend, and allows him to contest it without fear of double jeopardy.”). We therefore detect no error in the aggravated identity theft counts of the indictment.
B. In Camera Review of Potential Brady Material
José next faults the district court for rejecting his request to order the government to turn over documents José claims were potentially exculpatory. See Brady v. Maryland, 373 U.S. 83, 87, 831 S.Ct. 1194, 10 L.Ed.2d 215 (1963) (government has an obligation to disclose evidence in its possession favorable to a criminal defendant and material to guilt). In particular, José argues that he was entitled to materials related to a government search of the offices of one of the Medicare Advantage insurers he fraudulently billed, Medical Card System (“MCS”).
Both defendants filed separate pre-trial motions requesting specific exculpatory and impeachment material. The requested information included the following materials:
Any documents, reports, affidavits in support of search warrants, grand jury subpoenas, or other materials and information regarding any investigation of any wrongdoing by any health insurance company that processes any Medicare or other insurance claim that is the subject of the charges alleged in the indictment, including, but not limited to, MCS....
The district court referred the matter to a magistrate judge, who granted the defendants’ request subject to a protective order that restricted the disclosure and use of patients’ individually identifiable health information. The government did not disclose prior to trial any documents related to a search warrant executed at MCS. On the fifth day of trial, however, before the defendants cross-examined a fraud investigator at MCS, Carlos’s defense attorney renewed his request in light of press coverage of a government search of MCS [116]*116offices. The government agreed to review the MCS search documents during a pre-scheduled eight-day break in the trial, and to disclose any exculpatory or impeachment material, while complying with the protective order. On cross-examination, the MCS fraud investigator confirmed that government agents had searched the MCS office, but she did not speak with the agents and did not know whether the investigation was ongoing.
The government again produced no documents, and on the next day of trial, Carlos’s attorney asked that “the Court order them to produce those records or that they be submitted to the Court and that copies be left in the record under seal for future review, if necessary.” The government agreed to provide the MCS search warrant affidavit for the court’s in camera review, to determine if the search may have revealed information relevant to Carlos and José’s case. The next day, the district court informed counsel that-its “review of the search warrant, the application, and affidavit has completed, and I don’t think any of it has any relevance to this case.... [Y]our motion is denied.” The district court then denied Carlos’s motion to seal the search warrant, application, and affidavit and make those documents part of the record in this case, because the court was “worried about making it a part of this record even as a sealed document.” The district court and government noted that the documents could be made available to this court if necessary for appellate review. Shortly thereafter, José’s counsel joined Carlos’s motions.
On appeal, José asks us to review the search warrant, application, and affidavit to determine whether the district court erred in refusing to require disclosure by the government. We review a district court’s Brady determinations after its in camera review for an abuse of discretion. United States v. Rosario-Peralta, 175 F.3d 48, 57 (1st Cir.1999); see also United States v. Caro-Muñiz, 406 F.3d 22, 28-29 (1st Cir.2005).
We decline the invitation to join José on his fishing expedition. His theory about the relevance of the MCS documents is that those documents “could have very well” contained instructions from MCS to physicians, including José, to submit false information on CMS 1500 Forms, thereby corroborating José’s testimony that he used inaccurate billing codes based on instructions from health insurance companies. How such evidence would have exonerated José from billing for urological services performed on women whom he did not treat is a complete mystery concerning which José offers no insight. Additionally, José points to nothing that suggests that the government’s search of MCS had anything to do with its telling doctors to use incorrect billing codes. Hence his theory of relevance amounts to little more than “mere speculation.” United States v. Prochilo, 629 F.3d 264, 269 (1st Cir.2011). The district court therefore would have acted well within its discretion even if it had refused to conduct the in camera review in the first place. See id. at 268-69 (“To justify [in camera] review, the defendant must make some showing that the materials in question could contain favorable, material evidence. This showing cannot consist of mere speculation.” (citations omitted)). Because José’s request amounts to no more than a “shot in the dark,” United States v. Espinal-Almeida, 699 F.3d 588, 618 (1st Cir.2012), we find it unnecessary to review the sealed documents that the district court viewed in camera.
C. Challenges to the Jury Instructions
1. Prior Knowledge for Aiding and Abetting
José claims that the district court erred in failing to instruct the jury that, in [117]*117order to convict him of aiding and abetting aggravated identity theft, the jury had to find that José had “prior knowledge” of one purported element of aggravated identity theft: that the patients’ identifying information was obtained without lawful authority.18 In support of this argument, José cites Rosemond v. United States, — U.S.-, 134 S.Ct. 1240, 188 L.Ed.2d 248 (2014), in which the Supreme Court held that, to convict a defendant for aiding and abetting the knowing use of a firearm during and in relation to a drug trafficking crime under 18 U.S.C. § 924(c), the government must prove that the defendant had advance knowledge of each element of the offense (i.e., the drug part and the gun part). Id. at 1248-49.
José did not request that the district court give the instructions he now claims it should have given. To the contrary, he asked the court to give an instruction materially the same as that which it gave. José therefore arguably waived this challenge to the jury instructions. See United States v. Alberico, 559 F.3d 24, 27 (1st Cir.2009).
Even if José did not waive the argument, his failure to object would justify only plain error review, see Fed.R.Crim.P. 30(d), 52(b), a standard José fails to satisfy. See United States v. Duarte, 246 F.3d 56, 60 (1st Cir.2001) (“Review for plain error entails four showings: (1) that an error occurred (2) which was clear or obvious and which not only (3) affected the defendant’s substantial rights, but also (4) seriously impaired the fairness, integrity, or public reputation of judicial proceedings.”). The so-called element of which José says he needed prior knowledge— that the identifying information was initially obtained without lawful authority — is not actually ah element of the offense. Section 1028A punishes the knowing transfer, possession, or use without lawful authority of protected information, 18 U.S.C. § 1028A(a)(l), regardless of how that information was first obtained. United States v. Ozuna-Cabrera, 663 F.3d 496, 499 (1st Cir.2011) (“[Rjegardless of how the means of identification is actually obtained, if its subsequent use breaks the law ... it is violative of § 1028A(a)(l).”). Even if an instructional error had occurred, it could not have affected José’s substantial rights. The evidence overwhelmingly showed that José knew that he did not have the patients’ consent to use their information to bill for surgical and medical procedures he never performed.
2. Typographical Error in an Instruction
José also challenges a typographical error in the aggravated identity theft jury charge. The district court instructed the jury that the first element of aggravated identity theft was “that the defendants committed the crime of health care fraud as set forth in jury instruction number 11.” This instruction should have cross-referenced jury instruction number 12, listing the elements of health-care fraud, and not jury instruction number 11, which addressed vicarious liability for the acts and declarations of co-conspirators. There was no objection to this slip-up, and José concedes that review is for plain error only. The mistake here falls far short of the “exceedingly difficult to satisfy” plain error standard for jury instructions. United States v. Gonzalez-Velez, 466 F.3d 27, 35 (1st Cir.2006). The district court’s instruction correctly indicated that the predicate offense was health-care, fraud, and it would [118]*118have been obvious to the jury that the crime of health-care fraud was “set forth” in the instruction labeled as such, and not in the plainly inapplicable instruction titled “Acts and Declarations of Co-conspirators.” Moreover, given the weight and nature of the evidence against José, we doubt any confusion e'ngendered by the typographical error contributed to the jury’s verdict.
3. Success of the Conspiracy
José next challenges the district court’s refusal to instruct the jury that the government needed to prove the success of the conspiracy. This refusal, José contends, resulted in both a constructive amendment and prejudicial variance. José acknowledges that the government ordinarily does not need to prove the success of a conspiracy. See United States v. Paret-Ruiz, 567 F.3d 1, 6 (1st Cir.2009). According to José, though, the government committed itself to proving success by charging in the indictment that the object of the conspiracy was for the defendants to “enrich themselves.”19
No constructive amendment occurred here. “[A] constructive amendment occurs where the crime charged has been altered, either literally or in effect, after the grand jury' last passed upon it.” United States v. Mubayyid, 658 F.3d 35, 49 (1st Cir.2011) (internal quotation marks omitted). There was no change to the statutory elements of the offense. See id. at 51 (“[0]ur practice has been to look to statutory elements in response to claims by defendants that ‘the crime charged’ has been changed.”).20
Nor was there any variance between the charged crime and evidence at trial, let alone a variance that was prejudicial. See id. at 48 (“A variance occurs when the facts proved at trial differ materially from those alleged in the indictment without altering the crime charged.”). While there was no evidence that Carlos made even a penny as a result of José’s fraud, the government established that José himself billed Medicare for more than $3,500,000, and that Medicare paid him hundreds of thousands of dollars. José implausibly responds that those sums do not necessarily show enrichment without evidence of his “costs or overhead.” We think a jury could infer that José’s costs were low, and certainly less than the amounts he received, given that he did not actually perform the procedures for which he billed Medicare.21
IV. Conclusion
We vacate Carlos’s convictions on all counts for lack of sufficient evidence, and remand for entry of judgment of acquittal. Finding no error with respect to José, we affirm his convictions.