No, I understand precisely what you're trying to say. Based on my (admittedly anecdotal) experience applying to colleges and working (however briefly) in Financial Aid at MIT, it was not a 20% blanket by any stretch; each case was treated individually and there was an explicit focus on ensuring students were not saddled with insane amounts of debt.
There were exceptions, particularly for wealthy folks and people who were 'on the line' income-wise, but the majority got significant financial aid.
Just to give you an idea, from MIT's stats[1]:
* Average need-based MIT scholarship: $47,593
* Students awarded a need-based MIT scholarship: 59%
* Students attending tuition-free: 31%
* Class of 2019 graduates with no student loan debt: 76%
* Average student loan debt for those who borrowed: $23,226
The trope that the expensive schools are the cause of the massive student loan debt problem is just that; a trope. When only 24% of the class graduates with any debt at all, I'm not convinced MIT (and similar) are the problem. This is largely due to MIT and similar schools having massive endowments from which they can draw for Financial Aid; there are cheaper schools, certainly, but they have coffers that are less deep (referring to private schools), meaning students end up having to take more debt.
[1] https://web.mit.edu/facts/tuition.html