I wouldn’t describe it quite like that, and remember that much of Cornell is state funded.
Brown does not have nearly the same riches as Princeton or Williams (the question is why Harvard and Yale aren’t as generous as Princeton!). They are in a situation where, to afford to be generous to the neediest - and IMO the are - they can’t afford to be generous to the slightly better off. The reality is that Brown has a huge middle class doughnut hole. It’s not greed. it’s just how the math works out if they want to increase access to more underprivileged kids.