I never claimed that Penn draws A LOT of students from HYPSM, but it draws at least comparable numbers to Duke without any merit scholarships. The point I was trying to make is that I doubt that the number of students who accept the AB scholarship over HYPSM and who actually do not need the financial aid, is significant. I could be wrong of course but this data is not available so who knows.
http://www.dukechronicle.com/article/2013/05/scholarship-yields-reflect-competition
In this article posted by someone above, the wording is rather vague on the matter. Also the article rather conflates the idea of not requesting aid and actually basing the decision of attending purely on the university quality rather than monetary value, which can be two very different things . A person can come from a solid middle, maybe upper-middle class background and thus afford to pay the full price for college so they haven’t applied for aid. However $250,000+ is a lot of money for a middle, low-end upper middle class family especially if there is more than 1 kid. So while they can afford the full price, when given the opportunity of full ride at a top school like Duke, choosing Duke becomes a very attractive alternative to HYPSM primarily due to monetary value.