You just can’t make up a coincidence like this.

On Thursday, the same day Louis Freeh, the former director of the F.B.I., issued his damning report about the cover-up of Jerry Sandusky’s sexual crimes by the Penn State hierarchy, the N.C.A.A. lowered the boom on — are you ready for this? — the California Institute of Technology.

One of the world’s great engineering schools, Caltech is never going to be mistaken for Penn State as an athletic force. With fewer than 1,000 undergraduates, it is a Division III school, which means, among other things, that it doesn’t grant athletic scholarships. Its basketball team ekes out about five wins a season, and its baseball team, according to The Times, has lost 227 games in a row. At Caltech, unlike your typical athletic powerhouse, “student-athletes” truly are students.

Part of being a student at Caltech means “shopping” for courses for the first three weeks of each trimester. Students are allowed to sample classes before they have to register for them. “During those three weeks,” read an N.C.A.A. press release issued on Thursday, “because they were not actually registered in some or all of the courses they are attending, some students were not enrolled on a full-time basis.” And part-time students, you see, are not allowed to play intercollegiate athletics. Between 2007 and 2010, according to the N.C.A.A., this happened with 30 athletes in 12 sports.

It would be hard to imagine a more frivolous violation of the rules — or one that could do less harm to the integrity of college sports. What’s more, Caltech turned itself in after a new athletic director realized that the practice of shopping for classes probably violated N.C.A.A. rules. Yet the punishment imposed on the school was severe: three years of probation, a postseason ban in a dozen sports, the erasure of wins and individual records that were gained with ineligible athletes, and more. Indeed, Caltech was cited for “a lack of institutional control,” which is pretty much the worst thing you can be accused of in N.C.A.A.-speak.

In the wake of the Freeh report, there has been a lot of speculation about what punishment the N.C.A.A. should impose on Penn State — and even whether the Sandusky scandal is within its purview. I’m in the camp that says the N.C.A.A. should throw the book at Penn State. The legal system will take care of whether others besides Sandusky deserve to go to prison for failing to report his predatory behavior. Penn State itself will almost surely finish the painful process of removing the halo from the head of its late coach, Joe Paterno, which the Freeh report has begun. But only the N.C.A.A. can impose the so-called death penalty, forcing Penn State to shut down its football program for a period of time. Yes, it would make a mess of television schedules, not to mention the rest of Penn State’s athletic teams — which rely on the revenue that football generates — but it’s the only way to send the right message.

That message is this: no university should ever be as beholden to its football program as Penn State was. At other big-time sports schools, there are all kinds of daily hypocrisies that people avert their eyes from in the name of college football or men’s basketball. Sadly, we accept these hypocrisies as the price to be paid for the money college sports generates and the entertainment it provides.

But at Penn State, football was of such overweening importance — and Paterno was such a godlike figure — that a sexual predator was allowed to roam free because of his association with football. A janitor spots Sandusky in the shower with a boy but is afraid to say anything because crossing Paterno “would have been like going against the president of the United States.” Sandusky uses the lure of the football program to attract his victims. Paterno and others in the Penn State chain of command, in Freeh’s words, “repeatedly concealed critical facts relating to Sandusky’s child abuse” — to avoid bad publicity for the football program. A great university sold its soul to its football team.

As regular readers know, I don’t have much faith in the N.C.A.A. It has congealed into a bureaucracy that cares only about enforcing its rules, no matter how silly or retrograde. But here is a chance to put its money where its mouth is. The N.C.A.A. proclaims that part of its mission is to “integrate athletics into higher education.” If it really believes that, it will impose the death penalty on Penn State, to send a signal that no school should put football above its own integrity.

Anything less than that will send another signal entirely. Namely, that in the eyes of the N.C.A.A., what happened at Penn State is no worse than what happened at Caltech.