I'm sure that there are some colleges where other factors have greater influence on the behavior of the college. But for the vast majority, all that I've seen, the schools are operated exactly as you say.
The other factors are just a marketing trick. You know higher quality is a niche on its own --- and you have to seemingly ignore sales and concentrate on high ideals alone, to generate good sales in this niche. At least that's what works for industries other than education.