Having graduate from Stanford a few years back, I can clarify a couple rumors and start a few others:
1) Everyone at Stanford is rich? If only... Most of my circle of friends was middle class, maybe middle-upper. There were a lot of people at Stanford from lower socio-economic backgrounds. Usually somewhere between 10-15% of all students in a class are the first to go to college, and about 1/3 of those aren't coming from rags to riches (or even rags to middle-class) families.
2) $60k is the magic number to have everything paid for, including room and board, books, fees, etc. And that room and board part is expensive.
3) $100k only gets you tuition. Stanford estimates that it is $16.5k for things other than tuition. I can tell you that that is low. It's probably closer to $18-19k now.
4) Turns out in Stanford's system, the worst hit are upper-middle class families who won't borrow money or change their lifestyle to pay for their child's college. I graduated with $45k in student debt mostly because the parents gave me a fixed amount of money and I had to make the difference. Stanford doesn't help in cases like this - they just make you take out loans. But, that doesn't mean I wouldn't do it all over again.
So, it's not as simple cut-and-dry as some like to think it is. Stanford's large endowment certainly didn't help me much. And it didn't help some of my other friends much either with their individual cases. On the other hand, many of my friends who came from middle-class backgrounds were there only because of the endowment. So, you win some; you lose some.
The athletics programs are much the same. While there are athletic scholarships for some teams, most teams survive with "book scholarships," which basically means that books are paid for. Many of the athletes are on financial aid. I noticed that athletic scholarships in non-revenue sports were usually reserved for fifth year athletes when financial aid ran dry. Could be wrong about that, but I'd suspect that's how the department managed things.
It was often very difficult to be an athlete at Stanford. For example, Stanford counts on summer employment income from students. However, the athletes couldn't do anything related to their sport lest they be accused of accepting professional money and be banned by the NCAA. That's not a Stanford-only problem, but it has a pretty great impact on students who need summer income and are otherwise relegated to office work, waiting tables or, if they're lucky, an internship at a company that is flexible with their training schedule.
Take what you want from that ramble. Just trying to add a little insight, but only a little as I did not have a clear picture into the world of athletics financing.