It turns out there is such a law. The Solomon Amendment, passed in 1994, withdraws federal financing from any college with a “policy or practice” preventing the military from “maintaining, establishing or operating” R.O.T.C. on its campus. The law also takes financing away from colleges that bar military recruiting. The Defense Department hasn’t been shy about enforcing its right to recruit, going all the way to the Supreme Court and winning in Rumsfeld v. FAIR.

So if there are colleges that ban R.O.T.C., why aren’t they being punished?

The answer is that in all my research on the subject, I have found no universities that ban R.O.T.C., nor has the military initiated action against any institution for banning the program. We have grown accustomed to saying there are bans only because it fits with the assumption that certain colleges are unfriendly to the military.

It is true that many Ivy League colleges do not have R.O.T.C. detachments today. Forty years ago, the military started to close detachments in the Northeast and establish programs in the West and South.

This shift stems from a disagreement in the late 1960s between the Ivy League colleges and the military. Should R.O.T.C. have to comply with the host college’s rules for academic course content and professor qualifications? R.O.T.C. said no, colleges said yes, and the two had to agree to disagree. R.O.T.C. then walked away from Northeastern campuses.

While Harvard is often described as “expelling” R.O.T.C. in 1969, the story is more nuanced. After the military refused to meet Harvard’s standards on academic coursework, the faculty voted to relegate the program to an extracurricular activity, and the military decided to leave. But Harvard did not abolish the program, and it was only much later that people began to talk of a ban.