I think that top-tier private schools give lots of grants to low-income students who do well in high school, AS THEY SHOULD, these people have worked really hard with their limited resources to do well in high school, but I think what results is that the people in middle-income brackets have a tough time because only the really wealthy and the lower-income can do it financially.
As for financial safety schools, I have Penn State and maybe Indiana. Both of my parents are Indiana alumni so maybe I could get something from them? Idk.