Opinion for the Court filed by Circuit Judge STEPHEN F. WILLIAMS.
STEPHEN F. WILLIAMS, Circuit Judge:
Plaintiff-appellants Monmouth Medical Center and Staten Island University Hospital are acute-care facilities that receive payments under Medicare Part A for services to Medicare beneficiaries. Since 1983, the Secretary of Health and Human Services has made payments to cover hospital operating costs for inpatient care under the Prospective Payment System (“PPS”), which reimburses according to a uniform national rate schedule. See 42 U.S.C. § 1395ww(d). The two hospitals, because they serve a disproportionate share of low-income Medicare recipients, are eligible for “disproportionate share hospital” (“DSH”) adjustments to their PPS payments. See 42 U.S.C. § 1395ww(d)(5)(F). Monmouth and Staten Island sought the aid of the district court in an attempt to have their fiscal year (“FY”) 1993 and FY 1994 DSH payments recalculated, asserting jurisdiction under 42 U.S.C. § 1395oo(a)(l)(a), 28 U.S.C. § 1331, and 28 U.S.C. § 1361. The district court decided that the hospitals failed to follow the statutorily mandated procedure for appealing their payments, that 42 U.S.C. § 1395Ü precludes other review, and that, accordingly, it lacked subject matter jurisdiction. We reverse.
The Secretary of HHS has delegated authority to administer the Medicare Act to the Health Care Financing Administration (“HCFA”).
Determinations of payment amounts are in turn often delegated to fiscal intermediaries, generally private insurers that manage the payments for the Secretary. See 42 U.S.C. § 1395h. Estimated payments are made periodically and an annual accounting is done by the intermediary in the form of a Notice of Provider Reimbursement (“NPR”) based on a cost report submitted by the provider after the close of each fiscal year.
The Medicare Act has detailed instructions on the means for seeking review of payment determinations. Under 42 U.S.C. § 1395oo(a)(l)(A) a dissatisfied provider may appeal two types of “final determinations” to the Provider Reimbursement Review Board (“Board”). Clause (i) covers a fiscal intermediary’s final reimbursement decision, commonly the NPR, and clause (ii) covers a final determination of the Secretary regarding payments under 42 U.S.C. §§ 1395ww(b) or (d), including the DSH payments. Appeals are to be filed within 180 days of notice of the final determination.
Id.
§ 1395oo(a)(3). In either case, the decision of the Board is then reviewable by filing in district court within 60 days of notice of the decision, or by the Secretary’s own motion.
Id.
§ 1395oo(f). Section 1395Ü generally forecloses other avenues of review by incorporating the review-limiting provision of the Social Security Act, 42 U.S.C. § 405(h):
The findings and decision of the [Secretary of HHS] after a hearing shall be binding upon all individuals who were parties to such hearing. No findings of fact or decision of the [Secretary of HHS] shall be reviewed by any person, tribunal, or governmental agency except as herein provided. No action against the United States, the [Secretary of HHS], or any officer or employee thereof shall be brought under section 1331 or 1346 of title 28 to recover on any claim arising under this subchapter.
42 U.S.C. § 405(h).
The Secretary’s regulations provide three additional channels of administrative review. Under 42 CFR § 405.1841(b), a laterfiled request for Board review may be considered by the Board, provided that good cause is shown and the request is filed no more than three years after the NPR. The regulations also provide two possibilities for the reopening of a determination, again with a three-year limit. 42 CFR § 405.1885(a) provides for reopening, at the discretion of the decisionmaker, on the motion of the provider. Subsection (b) of that same regulation, which ultimately controls here,
mandates
reopening in one special circumstance. It directs that the decision
shall
be reopened and revised by the intermediary if ... the [HCFA] notifies the intermediary that such determination or decision is inconsistent with the applicable law, regulations, or general instructions issued by the [HCFA].
42 CFR § 405.1885(b) (emphasis added).
Under the statute authorizing DSH adjustments, eligibility for and calculation of the payment require the summing of two fractions. The numerator of one of these fractions calls for the number of inpatient days of patients who “were
eligible
for medical assistance under a State plan [i.e., Medicaid].” 42 U.S.C. § 1395ww(d)(5)(F)(vi)(II) (emphasis added). The Secretary promulgated a regulation on how to make the calculation and
has repeatedly amended it. See 42 CFR § 412.106 (1998) (version in force when original DSH calculations were made). At the same time, the Secretary published an interpretation of that rule in the Federal Register as part of the notice and comment rulemaking implementing the PPS. See 51 Fed.Reg. 16,772, 16,777 (May 6, 1986); 51 Fed.Reg. 31,454, 31,460 (September 3, 1986). Reading “who were eligible” as “ ‘who (for such days) were eligible’ ” the Secretary declared that “Medicaid covered days will include only those days for which benefits are
payable.”
51 Fed.Reg. at 16,777/2-3 (emphasis added). This interpretation had the effect of reducing payments by limiting adjustments for patients who were
“eligible” for
Medicaid benefits under the natural reading of the word, but who, because of a particular state’s program, were not receiving such benefits on a given day.
Neither hospital timely availed itself of the right to appeal the NPRs in question. But other providers did. The Secretary’s interpretation fared poorly, being struck down in four of our sister circuits. See
Cabell Huntington Hosp. v. Shalala,
101 F.3d 984 (4th Cir.1996);
Legacy Emanuel Hosp. & Health Ctr. v. Shalala,
97 F.3d 1261 (9th Cir.1996);
Deaconess Health Serv. Corp. v. Shalala,
83 F.3d 1041 (8th Cir.1996);
Jewish Hosp., Inc. v. Secretary of Health and Human Services,
19 F.3d 270 (6th Cir.1994). In light of these decisions, the Administrator of HCFA issued a ruling that rescinded the Secretary’s challenged interpretation nationwide. See Health Care Financing Administration Ruling 97-2 (February 27, 1997) (“HCFAR 97-2”). The ruling established a new interpretation more favorable to hospitals, providing that Medicaid eligible days would be counted “whether or not the hospital received payment for those inpatient hospital services.”
Id.
The new interpretation was to be effective in the month of its publication and applied to all as yet unsettled cost reports and all cases in which “jurisdictionally proper” appeals were still pending. See
id.
The ruling explicitly foreclosed retrospective application: “We will not reopen settled cost reports based on this issue.” See
id.
Like all such rulings, HCFAR 97-2 was issued without notice or opportunity for comment.
The hospitals nonetheless sought recalculation of their DSH payments, filing with their intermediaries for reopening well within the three years required by § 405.1885. Their respective intermediaries denied the requests, citing HCFAR 97-2. Both hospitals also sought Board review in attempts to satisfy the jurisdictional requirements of 42 U.S.C. § 1395oo. They filed their appeals within 180 days of the publication of HCFAR 97-2, but the intermediaries objected that the trigger event was each hospital’s NPR, not HCFAR 97-2. In response, the hospitals invoked § 405.1841(b), which allows extension of the time limit for “good cause.” They argued that the delay was unavoidable because they could not have anticipated HCFAR 97-2’s refusal to grant reopening. In separate letters to the providers, the Board stated that “your rationale for late filing does not constitute good cause” and that it lacked jurisdiction to hear the appeals. Both hospitals sought review in the district court. We review the district court’s jurisdictional determination
de novo.
See
Moore v. Valder,
65 F.3d 189, 196 (D.C.Cir.1995). Although we eventually conclude that we have jurisdiction under 42 U.S.C. § 1361, we must first examine all other possible avenues of relief to ensure that the hospitals have fully exhausted those which were available.
The hospitals first invoke the jurisdiction of the district court under 42 U.S.C. § 1395oo(f) to review the Board’s
denial of their appeals. Having acknowledged that their appeals were untimely with respect to the NPRs, they frame the appeals here as challenges to the reopening prohibition in HCFAR 97-2. At issue is whether the Board could properly consider such an attack. As noted above, clause (i) of § 1395oo(a)(l)(A) gives the Board jurisdiction to review final reimbursement determinations by intermediaries. But it appears that neither of the hospitals framed its appeal as being from its intermediary’s non-reopening decision, and an HCFA Ruling is
not
the action of an intermediary. Staten Island did not even request reopening until three months after it sought Board review. And Monmouth, while it tried for reopening before making its appeal to the board, made absolutely no mention of its intermediary or its reopening request in its appeal to the Board.
Clause (ii), which applies to final determinations of the Secretary regarding a provider’s PPS calculations, brings jurisdiction no nearer. In
Washington Hosp. Center v. Bowen,
795 F.2d 139 (D.C.Cir.1986), we determined that a pre-NPR challenge could be brought where the Secretary had firmly established “the only variable factor in the final determination as to the amount of payment under § 1395ww(d).”
Id.
at 147. There the Secretary had determined the individual hospitals’ “target amount,” the erstwhile variable factor, thereby fixing their payment amounts under the PPS. Even after concluding, as we do below, that HCFAR 97-2 triggered mandatory reopening under § 405.1885(b), we fail to see how an attempt by the Secretary to establish a general policy against reopening in any way resembles a final determination “as to the
amount of
payment,” the only kind of determination for which clause (ii) creates a right of appeal to the Board. The hospitals argue that the blanket application of the ruling is irrelevant, because it directly affects their claims specifically. That may be true, but the effect is merely to purport to alter the procedures by which they may seek a new final determination; it does not itself either establish or alter their “disproportionate patient percentage” or the amount of payment they receive under PPS.
Our conclusion that the hospitals’ appeals to the Board fit neither clause (i) nor clause (ii) is at least consistent with, if not required by, the Supreme Court’s recent opinion in
Your Home Visiting Nurse Services, Inc. v. Shalala,
525 U.S. 449, 119 S.Ct. 930, 142 L.Ed.2d 919 (1999). In that case, the Court reviewed a discretionary decision under § 405.1885(a) not to reopen a clause (i) determination, finding that such a refusal did not itself qualify as a clause (i) determination. It relied on
Califano v. Sanders,
430 U.S. 99, 97 S.Ct. 980, 51 L.Ed.2d 192 (1977), in which it held that judicial review is not available for the Secretary’s decision not to reopen a claim for benefits under the Social Security Act.
Sanders,
the Court pointed out, relied in turn on two factors: “that the opportunity to reopen a benefit adjudication was afforded only by regulation and not by the Social Security Act itself; and that judicial review of a reopening denial would frustrate the statutory purpose of imposing a 60-day limit on judicial review of the Secretary’s final decision.”
Your Home,
525 U.S. at 454, 119 S.Ct. 930. The
Your Home
Court also concluded that the absence of Board review would not deprive petitioners there of a suitable opportunity for “ ‘retroactive corrective adjustment! ]’ ” because they had an initial opportunity to appeal their NPRs, plus a
chance
to secure discretionary reopening by the intermediary.
Id.
(citing 42 U.S.C. § 1395x(v)(1)(A)(ii)).
One might argue that where a provider is seeking reopening under § 405.1885(b),
the
Sanders
concern about the finality of decision is lessened, inasmuch as such cases will be relatively few in number; they arise only if the HCFA determines that a prior decision or set of decisions is inconsistent with applicable law. But it would still remain unclear how this distinction would change the character of the reopening decision itself from “not a final determination” to “final determination.” And of course it should make no difference if the analysis arises out of clause (i) or clause (ii). In any event, we reserve our own final determination on this issue for a case in which it is more clearly presented; here HCFAR 97-2 can in no way be mistaken for a final determination for the purposes of judicial review under §§ 1395oo(a) & (f).
The hospitals nonetheless argue that our opinion in
Washington Hospital Center
and the HCFA’s application of it in
National Medical Enterprises Malpractice PPS Group Appeal,
Case No. 87-5050G, HCFA Adm. Dec. (Oct. 5, 1988), together compel the interpretation that clause (ii) creates a right to Board review 180 days after the “issuance, modification, or invalidation of a HCFAR.” App. Open. Br. at 48. They do no such thing.
Washington Hospital Center
held invalid HCFAR 84-1, which had barred appeal of PPS determinations until after an NPR was issued. Providers in
National Medical Enterprises
sought Board review for their payments in the wake of that case, but submitted their appeal more than 180 days from the issuance of our decision. The Administrator’s decision did indeed suggest that a more timely appeal would have been successful, but that conclusion was dependent on the peculiar operation of HCFAR 84-1, which had previously operated as a bar on properly filed appeals of right. See
National Medical Enterprises
at 3. In the absence of HCFAR 97-2 the hospitals would not have had recourse to the Board, as they have already acknowledged.
The hospitals next seek jurisdiction under 28 U.S.C. § 1331 for review of the reopening preclusion in HCFAR 97-2. Such review could not be more plainly off limits under 42 U.S.C. § 405(h), which explicitly withholds § 1331 jurisdiction for “any claim arising under this title.” The Supreme Court has consistently interpreted this phrase broadly, such that jurisdiction is barred when “ ‘both the standing and the substantive basis for the presentation’ of the claims” is the Medicare Act.
Heckler v. Ringer,
466 U.S. 602, 615, 104 S.Ct. 2013, 80 L.Ed.2d 622 (1984) (quoting
Weinberger v. Salfi,
422 U.S. 749, 760-61, 95 S.Ct. 2457, 45 L.Ed.2d 522 (1975)). Thus, in
Ringer,
the Court declared that plaintiffs seeking to overturn an HCFA ruling that would limit their recovery for a particular type of surgery could do so only in the context of the statutorily authorized process for review. This applied with equal force to the plaintiff who had not yet undergone the surgery and therefore had, as yet, no claim for reimbursement. See
id.
at 620. That the plaintiffs there were not seeking a specific monetary award was irrelevant. The ultimate goal for those plaintiffs, as for the hospitals here, was the recovery of additional sums under the Medicare Act. See
id.
at 615-16.
The hospitals make a plausible argument that jurisdiction may be had under the limited exception to § 405(h) carved out by
Bowen v. Michigan Academy of Family Physicians,
476 U.S. 667, 106 S.Ct. 2133, 90 L.Ed.2d 623 (1986), as interpreted by
Shalala v. Illinois Council on Long Term Care, Inc.,
529 U.S. 1, 120 S.Ct. 1084, 146 L.Ed.2d 1 (2000). In
Michigan Academy
the Court, concluding that Congress had incorporated § 405(h)
mutatis mutandis
into the Medicare Act, allowed a challenge to certain Medicare procedural regulations, reading § 405(h) as limiting review of determinations but not of “the Secretary’s instructions and
regulations.” 476 U.S. at 680, 106 S.Ct. 2133.
Illinois Council,
however, clarified
“Michigan Academy
as
holding
that § 1395ii does not apply § 405(h) where application of § 405(h) would not simply channel review through the agency, but would mean no review at all.” 529 U.S. at 19, 120 S.Ct. 1084. The hospitals here argue that, because they no longer have jurisdictionally valid claims before the Board and because HCFAR 97-2 would not in any event apply to them if they did, they will never have the opportunity to challenge that ruling. That seems like a plausible outcome. But despite the intermediaries’ rebanee on HCFAR 97-2, the ruling is separate from their denials of reopening, and under the Secretary’s regulations, only the intermediaries have the jurisdiction to reopen. 42 C.F.R § 405.1885(c). Jurisdiction to review the ruling would do nothing to provide jurisdiction over the intermediaries’ denials, which would stand unchanged — and no longer susceptible to automatic reopening, given the expiration of the three-year period for reopenings under § 405.1885(b).
The hospitals lastly seek jurisdiction under 28. U.S.C. § 1361 and relief ordering the intermediaries to reopen their determinations. The Supreme Court has on several occasions expressly reserved the question of whether § 1361 jurisdiction is precluded by § 405(h). See
Your Home,
525 U.S. at 456-57 n. 3, 119 S.Ct. 930;
Ringer,
466 U.S. at 616-17, 104 S.Ct. 2013. But this court has previously determined that § 1361 jurisdiction is not barred, see
Ganem v. Heckler,
746 F.2d 844, 850-52 (D.C.Cir.1984), joining the virtual unanimity of circuit courts. See, e.g.,
Burnett v. Bowen,
830 F.2d 731, 737-38 (7th Cir.1987);
Belles v. Schweiker,
720 F.2d 509, 511-13 (8th Cir.1983). Of course, to maintain an action under § 1361, a plaintiff must both exhaust administrative remedies and show a clear non-discretionary duty.
Ringer,
466 U.S. at 616-17, 104 S.Ct. 2013.
Neither party questions our ability to provide relief in the absence of the intermediaries as parties to this lawsuit, but we note that their non-joinder does not undermine our jurisdiction. The intermediaries are agents of the Secretary charged with the relevant duties under the Medicare Act and its regulations, and, as such, they may properly be bound by a writ of mandamus against the Secretary. See
United States ex rel. Rahman v. Oncology Associates,
198 F.3d 502, 511 (4th Cir.1999); Fed.R.Civ.P. 65(d).
The hospitals argue that 42 CFR § 405.1885(b) was triggered by HCFAR 97-2 and that the intermediaries therefore had a non-discretionary duty to reopen their determinations. The Secretary responds that the choice of whether or not to advise providers that a regulation is “inconsistent with the applicable law,” thereby triggering the intermediaries’ mandatory reopening duty under § 405.1885(b), is committed to the non-reviewable discretion of the Secretary. But the issue is not whether we may review the choice to advise or not advise as to consistency with applicable law; it is whether the Secretary, acting through the HCFA Administrator, in effect announced a finding of inconsistency (even while purporting to veto reopening).
To be sure, HCFAR 97-2 studiously avoided using the magic words “inconsistent with the applicable law,” and instead called the earlier interpretation “contrary to the applicable law in four judicial circuits.” HCFAR 97-2. The Secretary argues that HCFAR 97-2 merely “acquiesced prospectively,” in the interests of national uniformity, without actually admitting its illegality. But HCFAR 97-2 also purports to change an existing interpretation, and under the law of this circuit
altering an interpretive rule (interpreting an agency regulation) requires notice and opportunity for comment unless, of course, the original interpretation was invalid and therefore a nullity (as discussed below).
The Medicare Act places notice and comment requirements on the Secretary’s substantive rulemaking similar to those created by the APA. See 42 U.S.C. § 1395hh(b); 5 U.S.C. § 553(b). We have not had opportunity to decide whether the Medicare Act requirement of notice and comment for “changes [of] a substantive legal standard” creates a more stringent obligation or whether it somehow changes the dividing line between legislative and interpretive rules.
But it seems fair to infer that, as the Medicare Act was drafted after the APA, § 1385hh(c)’s reference to “interpretive rules” without any further definition adopted an exemption at least
similar
in scope to that of the APA. See
Warder v. Shalala,
149 F.3d 73, 79 n. 4 (1st Cir.1998). We see no reason to explore the possibility of a distinction here, as HCFAR 97-2 appears to have none of the indicia that would lead us to think it a legislative rule under the APA. See, generally,
American Mining Congress v. Mine Safety & Health Admin.,
995 F.2d 1106, 1108-12 (D.C.Cir.1993). In the absence of HCFAR 97-2 or its predecessor interpretation, there would still be an “adequate legislative basis for ... agency action.”
Id.
at 1112. The definition of eligible inpatient days is merely an “elucidation of rights and duties created by Congress” and the Secretary’s legislative rule.
Health Ins. Ass’n of America, Inc. v. Shalala,
23 F.3d 412, 423 (citing
American Mining Congress,
995 F.2d at 1109-10)).
But characterization as an interpretive rule does not relieve the Secretary of notice and comment requirements when a valid interpretation exists. In
Paralyzed Veterans of America v. D.C. Arena L.P.,
117 F.3d 579, 586 (D.C.Cir.(1997), we concluded that: “Once an agency gives its regulation an interpretation, it can only change that interpretation as it would formally modify the regulation itself: through the process of notice and comment rule-making.” See also
Alaska Professional Hunters Ass’n. v. Federal Aviation Administration,
177 F.3d 1030, 1033-34 (D.C.Cir.1999);
Shell Offshore Inc. v. Babbitt,
238 F.3d 622, 629 (5th Cir.2001). Here, a valid rule interpreting a regulation was clearly in play, and it was modified by HCFAR 97-2.
The new interpretation established by HCFAR 97-2 would therefore be unlawful absent notice and comment rulemaking, unless the original interpretation was itself invalid. See
Dixon v. United States,
381 U.S. 68, 74, 85 S.Ct. 1301, 14 L.Ed.2d 223 (1965) (“A regulation which ... operates to create a rule out of harmony with the statute, is a mere nullity.”) (internal citations omitted). As a general rule, it is for the courts to determine whether or not a regulation is invalid. As four circuits have already done so, it certainly can’t have been improper for the Secretary to concede the invalidity nationally. See
Independent Petroleum Ass’n of America v. Babbitt,
92 F.3d 1248, 1260 n. 3 (D.C.Cir.1996).
Concluding that the Secretary
did
in fact give notice of the interpretation’s inconsistency with applicable law, we also find that § 405.1885(b) imposed a clear duty on intermediaries to reopen DSH payment determinations for the hospitals. The portion of HCFAR 97-2 that conflicts
with that duty is simply inapplicable. In addition, we think it insignificant that, because of the Secretary’s own three year limitation, reopening would not be available if sought today. Although mandamus is classified as a legal remedy, its issuance is largely controlled by equitable principles. See
Duncan Townsite Co. v. Lane,
245 U.S. 308, 312, 38 S.Ct. 99, 62 L.Ed. 309 (1917). Since both hospitals were within the three-year mark when they made their requests for reopening, they are entitled to the reopening that was due them at that time. Cf.
Burnett,
830 F.2d at 736-41
&
n. 7.
The Secretary argues that the hospitals have failed to exhaust their remedies, because they failed to file proper appeals of their NPRs under § 1395oo(a). But that fact is hardly relevant here. The question is whether they have done all they can to vindicate their right to reopening. We have already shown above how all other avenues of relief are either foreclosed or futile.
Finally, the Secretary half-heartedly suggests that the hospitals may have waived mandamus jurisdiction by failing to specify § 1361 as one of the bases for jurisdiction until their response to the Secretary’s motion to dismiss. But the Secretary does not contend (apart from the arguments rejected above) that the hospitals failed to allege sufficient facts to support their mandamus claim, the essential test for legal sufficiency.
Richardson v. U.S.,
193 F.3d 545, 549 (D.C.Cir.1999). Nor does the Secretary argue that the government was in any way prejudiced by the trustees’ failure to list § 1361 in their complaints. The government has at best identified a procedural failing that would easily have been remedied by a request to amend the complaints that in no way affects our authority to consider issuance of a writ. See
Caribbean Broadcasting System, Ltd. v. Cable & Wireless P.L.C.,
148 F.3d 1080, 1083-84 (D.C.Cir.1998); Fed. R. Civ. P. 15(a). Indeed courts can treat certain requests for mandatory injunctions as petitions for a writ of mandamus, see, e.g.,
National Wildlife Federation v. U.S.,
626 F.2d 917, 918 n.1 (D.C.Cir.1980), and habeas petitions as ones for mandamus, see, e.g.,
United States ex rel. Schonbrun v. Commanding Officer,
403 F.2d 371, 374 (2d Cir.1968);
Long v. Parker,
390 F.2d 816, 818-19 (3d Cir.1968).
Accordingly, the judgment of the district court is reversed and the case remanded for further proceedings consistent with this opinion.
So ordered.