I will add that, after two sons at private schools with full financial aid guarantees, it has been the case that we could afford what they said we could afford, even if I was sometimes dubious when we got the annual financial aid calculation. Two schools calculate need quite differently, too. Your situation will vary from one year to the next, which is why they re-calculate it each year - a huge pain each January, but I see why they do it that way.
I think D1 and D2 schools with athletic scholarships, but with no guarantee of financial aid, would be quite different though. On this site, it's always pointed out that if you have no athletic scholarship, you can be easily cut, especially in this age of over-recruiting. I have seen it play out that way with kids who had financial need scholarships. That is especially brutal.