That's very much the ideal of the SAT, to draw out kids who are bright but haven't shown in through grades. It does happen. Statistically however, GPA is still a better predictor. It's just not the only one, and the SAT is overrated—hence even its creator talking about reform (again). My (totally unscientific) experience has been that a lot of the super-groomed kids don't come across so great. Having a soul is valuable too.
Ideally of course you have good grades *and* SAT scores! My kid has, to put it mildly, a very wide spread between SATs and GPA. I have no idea what the schools will think. They *are* in fact looking to GPA more and more. I think they are aware of the reputations of a great many schools and of grade inflation. Like you, I went to a prep school where everyone went to college, and its reputation stood for a lot. And straight A's in all AP classes at a school people have heard of is a fair criterion.
I think most admissions decisions are made on relatively little info and reflection. A lot of schools admit half or more of their applicants, and only a fraction actually matriculate. I doubt the 20-somethings doing most of the review are working too hard at analyzing the applicants. None of the schools my son applied to, for example, had interviews. On the other hand, yes, some schools get into it a little harder.
Oh BTW—congrats on pulling through the morass!