I can only speak for my field of education – chemical engineering – but save for a few counterexamples, many of the top rated schools are public schools. A Stanford undergraduate degree holds no more weight than a degree from the University of Illinois, for example.
As long as you are a good student in an accredited program, you can cherry pick your graduate schools – even the top ones – because your competition is greatly limited. On top of that, since you are covered by a stipend the tuition is not a factor. Not that a graduate degree automatically means a lot, but I digress.
I realize this isn’t a typical situation, but unless you are going to law school, I think the expensive school thing never will pay off. My better half may disagree with me, of course.