That’s not correct. Penn and Cornell will meet full demonstrated need as well. NYU will offer aid, but I don’t know if they claim to meet full need. But Penn, Cornell, and NYU are need aware for admissions, while Harvard is need blind. All are very difficult to be admitted to.
But I need to add the caveat for all schools that claim to meet demonstrated need - it’s their calculation of your need, not your desire of what you want.
Berkeley will give zero money, which will be the case for most public universities