It depends on the school. I know at Bowdoin, the money spent per student is even higher than full sticker price. And I believe they use their endowment for need based aid. I read a report from Kenyon that said a pretty big percent of tuition revenue was funneled back into need based financial aid so it was clear that a family paying full price at Kenyon was indeed funding need based financial aid for other families.
My guess is that, in general, schools with really large endowments don’t redistribute tuition dollars to families will get need based aid. I guess it’s good to know. If it bothers a family paying full price then they would consider where their money is going but a good point is made that diversity is a good thing and it benefits the full pay kids too.