As the Rumsfeld v. FAIR opinion noted,
When law schools began restricting the access of military recruiters to their students because of disagreement with the Government's policy on homosexuals in the military, Congress responded by enacting the Solomon Amendment. That provision specifies that if any part of an institution of higher education denies military recruiters access equal to that provided other recruiters, the entire institution would lose certain federal funds. The law schools responded by suing, alleging that the Solomon Amendment infringed their First Amendment freedoms of speech [including freedom from speech compulsion] and association.
But the Court expressly declined to rely on the government's extra power as subsidizer, and instead held that the government could impose the same rules even without a funding hook:
Congress' power to regulate military recruiting under the Solomon Amendment is arguably greater because universities are free to decline the federal funds. In Grove City College v. Bell (1984), we rejected a private college's claim that conditioning federal funds on its compliance with Title IX of the Education Amendments of 1972 violated the First Amendment. We thought this argument "warrant[ed] only brief consideration" because "Congress is free to attach reasonable and unambiguous conditions to federal financial assistance that educational institutions are not obligated to accept." We concluded that no First Amendment violation had occurred—without reviewing the substance of the First Amendment claims—because Grove City could decline the Government's funds.
Other decisions, however, recognize a limit on Congress' ability to place conditions on the receipt of funds. We recently held that "'the government may not deny a benefit to a person on a basis that infringes his constitutionally protected ... freedom of speech even if he has no entitlement to that benefit.'" United States v. American Library Assn., Inc. (2003). Under this principle, known as the unconstitutional conditions doctrine, the Solomon Amendment would be unconstitutional if Congress could not directly require universities to provide military recruiters equal access to their students.
This case does not require us to determine when a condition placed on university funding goes beyond the "reasonable" choice offered in Grove City and becomes an unconstitutional condition. It is clear that a funding condition cannot be unconstitutional if it could be constitutionally imposed directly. Because the First Amendment would not prevent Congress from directly imposing the Solomon Amendment's access requirement, the statute does not place an unconstitutional condition on the receipt of federal funds.
Maybe the Court got it right in FAIR and maybe it got it wrong; and maybe it should have only evaluated the Solomon Amendment as a funding condition, and not decided whether a similar rule "could be constitutionally imposed directly." But that's what FAIR actually did decide.