The academies are just different, and I'm willing to think that even as obtuse a body as the NCAA has some special rules for them.
Every student in the entire institution is on full scholarship, plus a stipend. That stipend thing doesn't run afoul of NCAA rules because it isn't an extra benefit...everybody, whether they play sports or not, gets it.
I don't know how they handle the walk-on / scholarshipped athlete / limitation on signees and rosters. And as another poster pointed out, they lose a bunch of the class between the sophomore and junior years, when the military obligation kicks in. So how they handle the APR thing, I don't know either. But I have to believe there is special dispensation on both of these fronts, specifically applicable to only them.
Here's a fun thing -- if you come back for your junior year, but for whatever long story reason, you don't graduate with your class, you still owe the military obligation....only you'll serve it as an enlisted man. The officer's commission comes only with your diploma.
And the diploma is recognized as an elite one. The ranks of corporate America are chock full with academy graduates. The combination of smarts, education, focus, self-discipline, leadership, and ability to navigate political waters, translates exceptionally well to large corporations.
Like many of you, I've often wondered why Army is so far behind the other two. They have the same requirements and same demands as Air Force and Navy. Why they're not better, I don't know.