
532 F.3d 578 (2008)
ALDEN MANAGEMENT SERVICES, INC., Plaintiff-Appellant,
v.
Elaine CHAO, Secretary of Labor, Defendant-Appellee.
No. 07-3828.
United States Court of Appeals, Seventh Circuit.
Argued June 2, 2008.
Decided June 25, 2008.
F. Thomas Hecht, Kathleen Holper Champagne (argued), Ungaretti & Harris, Chicago, IL, for Plaintiff-Appellant.
*580 Samuel S. Miller (argued), Office of the United States Attorney, Chicago, IL, for Defendant-Appellee.
Before EASTERBROOK, Chief Judge, and ROVNER and WOOD, Circuit Judges.
*579 EASTERBROOK, Chief Judge.
The Immigration Nursing Relief Act of 1989, 8 U.S.C. §§ 1101(a)(15)(H)(i)(a), 1182(m), allowed hospitals and other medical facilities to secure H-1A visas for foreign nurses to work in the United States. (This program ended in 1997. Its replacement is 8 U.S.C. § 1101(a)(15)(H)(1)(c). That change does not affect the current controversy.) Visas issued under the Act if the employer attested that more nurses were needed, that employment of foreign nurses would not adversely affect employment of U.S. citizens, and that the foreign nurses would receive the same pay as citizens employed as registered nurses at the same facilities. Visas in this program generally lasted for five years and were not renewable. (In other words, the program did not support immigration.)
Alden Management Services, which operates seven nursing homes in or near Chicago, certified its need for foreign nurses and eventually hired 119 from the Philippines. It did not, however, pay them as much as it paid registered nurses who are U.S. citizens. When the State Department grew concerned in 1995 that some representations made to secure the visas may have been incorrect, it sent a telegram to the Secretary of Labor, who administers the program once the nurses are in the United States. The Secretary opened an investigation. After an unduly protracted series of hearings and administrative appeals, the Secretary concluded that Alden had paid the nurses less than their due. She ordered Alden to make good the shortfall for the entire period that the nurses had been employed under H-1A visas.
In this suit, Alden does not contest any of the agency's factual findings. Nonetheless, it insists, the back-pay order is invalid because neither a foreign nurse nor any domestic nurse or union complained, and because the back-pay period should have been two years at most, rather than the whole of the nurses' employment. The district court entered judgment for the Secretary. 529 F.Supp.2d 882 (N.D.Ill. 2007).
The Act requires the Secretary to establish a system for resolving complaints:
The Secretary of Labor shall establish a process, including reasonable time limits, for the receipt, investigation, and disposition of complaints respecting a facility's failure to meet conditions attested to or a facility's misrepresentation of a material fact in an attestation. Complaints may be filed by any aggrieved person or organization (including bargaining representatives, associations deemed appropriate by the Secretary, and other aggrieved parties as determined under regulations of the Secretary). The Secretary shall conduct an investigation under this clause if there is reasonable cause to believe that a facility fails to meet conditions attested to. Subject to the time limits established under this clause, this subparagraph shall apply regardless of whether an attestation is expired or unexpired at the time a complaint is filed.
8 U.S.C. § 1182(m)(2)(E)(ii). Alden contends that the State Department is not an "aggrieved person or organization" and that the Secretary of Labor therefore "lacked jurisdiction" to do anything in response to the State Department's telegram.
*581 Section 1182(m)(2)(E)(ii) gives an "aggrieved person or organization" a legal entitlement to administrative action. We need not decide whether the State Department is an "aggrieved" organization. Alden leaps from "if an aggrieved person complains, then the Secretary must act" to "the Secretary may act only if an aggrieved person complains". The statute says the former but not the latter. Treating "there is a private right to at least X" to mean "the agency is forbidden to do more than X" is a logical error. "If A then B" (if a private victim complains, then a hearing must be held) differs from "only if A, then B" (only a private complaint allows a hearing). Alden confuses necessary and sufficient conditions. An aggrieved party's protest is sufficient to require an investigation but is not necessary. Nothing in § 1182(m)(2)(E)(ii), or anywhere else in the Act, limits the Secretary's ability to inquire into statutory compliance.
Federal agencies usually start investigations on their own; private complaints are neither necessary nor sufficient. The SEC can tell an investor to go jump in a lake, and the agency may limit its enforcement agenda to internally-generated cases; § 1182(m)(2)(E)(ii) says that the Secretary of Labor may turn a deaf ear to busybodies but not aggrieved persons. An obligation to act on behalf of domestic nurses injured by foreign competition does not prevent the Secretary from acting independently to ensure that employers follow the law. Administrative alertness and initiative do not transgress any federal statute and are usually thought marks of good government.
The Secretary's regulations provide that a private complaint is not necessary to an investigation. 20 C.F.R. § 655.400(b). That regulation does not contradict any part of the statute and could not be called arbitrary or capricious. Agency-initiated proceedings are routine. Under the National Labor Relations Act, for example, private parties may file charges but only a complaint by the General Counsel of the National Labor Relations Board starts the formal process  and the General Counsel may act even if no one has complained. 29 U.S.C. §§ 153(d), 160. Some statutes give private parties a right to be heard, but very few make that route exclusive. Although Title VII of the Civil Rights Act of 1964 usually requires a private charge, the Attorney General or any Commissioner of the EEOC may initiate a proceeding. See 42 U.S.C. § 2000e-5(b), (f). A system that makes a complaint by a private victim indispensable is conceivable, but § 1182(m)(2)(E)(ii) does not create one.
This leaves Alden's argument that the back-pay period should have been shorter. This argument, too, rests on a logical error. Alden apparently believes that that a period of limitation affects how long a damages period may run after the proceeding has begun, as well as how long before its commencement damages may go back. That is not how a statute of limitation works. The period specifies how far before the case begins the remedy may reach. See National Railroad Passenger Corp. v. Morgan, 536 U.S. 101, 122 S.Ct. 2061, 153 L.Ed.2d 106 (2002). It has nothing to do with whether a remedy may be awarded for time after the proceeding begins, during which the wrong continues. Once an administrative proceeding gets under way, back pay may be awarded for as long as the worker continues to receive less than the law requires. See, e.g., NLRB v. Ironworkers, 466 U.S. 720, 104 S.Ct. 2081, 80 L.Ed.2d 715 (1984); NLRB v. J.H. Rutter-Rex Manufacturing Co., 396 U.S. 258, 90 S.Ct. 417, 24 L.Ed.2d 405 (1969).
What's more, nothing in the Act establishes a period of limitations for the *582 Secretary's proceeding. Alden believes that the Secretary (or a court) should borrow a limit from another law, but a borrowing approach  which has been superseded for post-1990 federal statutes by 28 U.S.C. § 1658(a); Jones v. R.R. Donnelley & Sons Co., 541 U.S. 369, 124 S.Ct. 1836, 158 L.Ed.2d 645 (2004)  does not apply to administrative proceedings initiated by the national government. Unless a federal statute directly sets a time limit, there is no period of limitations for administrative enforcement actions. See BP America Production Co. v. Burton, 549 U.S. 84, 127 S.Ct. 638, 166 L.Ed.2d 494 (2006); Intercounty Construction Corp. v. Walter, 422 U.S. 1, 95 S.Ct. 2016, 44 L.Ed.2d 643 (1975).
According to Alden, the Secretary violated the due process clause of the fifth amendment by adopting and then abandoning several different, and incompatible, views about the appropriate back-pay period. We don't see what the Constitution has to do with this. The Administrative Procedure Act entitles private parties to fair hearings. 5 U.S.C. § 554(c). Cf. Rehman v. Gonzales, 441 F.3d 506 (7th Cir. 2006). Alden does not contend that the agency violated § 554 or any regulation by revising its legal arguments as the case proceeded. An agency that propounds a mistaken legal view not only may but also should correct it. Courts don't hold a party to its first legal theory. One does not plead law, see Bartholet v. Reishauer A.G. (Zürich), 953 F.2d 1073 (7th Cir. 1992), and under Fed.R.Civ.P. 54(c) the judgment awards the prevailing party its legal entitlement whether or not that party has correctly understood its rights and demanded exactly its legal due. Counsel for Alden acknowledges that Rule 54(c) is constitutional; if that is so it is impossible to see how the due process clause binds the Secretary to an early, and mistaken, view of the length of the back-pay period.
A belated shift in legal position could make the administrative decision arbitrary, and justify relief under the APA, if it prevented the private party from introducing facts that are material under the agency's new view but not its old one. That did not happen here, however. The agency decided during an interlocutory administrative appeal that foreign nurses are entitled to back pay for the entire length of their work under H-1A visas. It concluded that what matters is whether the foreign nurses received wages below those of domestic registered nurses, rather than the timing or content of Alden's attestations (which led to the H-1A visas). Alden then had another hearing. Alden deems this inadequate because the administrative law judge was bound by the appellate decision establishing the legal principles. But Alden had ample opportunity to adduce any facts that affected its back-pay obligation. Instead of demanding that the Secretary prove the relevant facts, Alden and the Secretary's lawyers stipulated how much back pay Alden owes under the Secretary's legal position. Whether the Secretary's position is correct is a subject open to decision in court. The goal of the hearing was to elicit all facts that matter, given the applicable law. That a statute, regulation, or higher tribunal tells an ALJ what legal rules to apply does not make an evidentiary hearing illusory.
The agency gave Alden an opportunity to be heard on all factual issues material to its ultimate decision. And, as we have concluded that the Secretary's legal position is correct, the judgment of the district court is
AFFIRMED.
