Is this still true? Most of the top schools today appear to have pretty generous aid compared to my undergrad, which was a state school. Only exception I can think of could be out of state public schools like Berkeley or Georgia Tech or CMU.

stanford provides need based aid. if your parents’ earnings are high enough to not qualify for full aid, but have financial circumstances that make it infeasible to attend, you get crunched.

Every year the ratio between talent and seats at elite schools grows. Elite schools don't grow with the size of the general population.