I went to an Ivy League college, and my parents are by no means rich, or even upper middle class. What happened was the college tried to use any excuse they could possibly find to deny "financial aid". One time I was denied because of a rounding error in my parents' tax returns.
Literally a rounding error. The only reason I managed to graduate was because a lawyer I happened to know threatened to sue the school.
If the Ivies want to say, "we're a school for the rich, tuition is $XXXK, put up the cash or don't come here", that is 100% their right as private institutions. But if they promise that aid will be provided to anyone who needs it, and they then revoke that promise on a whim when someone is already partway through their degree, they are lying bastards and need to be called out on it.