It's making a mistake if you go there for the wrong reasons. I think the way people look at it is, hey, wow, I can go here (free, in Stanford's case, I think), and get a nice shiny degree that says "Harvard" or "Stanford" on it. I don't think they're looking at the school, thinking, "Hey, Harvard has one of the top physics programs in the nation" or "Stanford's engineering is top-notch." And, because they are football players first and foremost, they're not getting the same hardcore Stanford education that the rest of the students go there to get. It's a huge disparity. (I think a lot less so at Harvard, because they don't hand out scholarships).
It's not like they have to go to Harvard or Stanford. Cal-Berkeley and Michigan are another two of the premier universities in the world. And an ivy league degree - while shiny and prestigious - is not a free ticket to riches.
You're right, though, in a sense: some circles definitely recognize the Ivy nameplate. But "ooh, shiny name" is, IMO, an awful reason to go somewhere, regardless of who you are. If education is really that important to them, they'd be looking at the UC's, UVA, Michigan, Texas, as well. Otherwise, they're fooling themselves - and maybe some others as well. I mean, look at the athletes you see playing football for Michigan, Cal, UCLA, USC, and so on. Are most of them there to take advantage of the world-class engineering program at Michigan and Cal (not that they'd have the time?), or are they getting through easy classes with the help of tutors and with the weight of the football program behind them.
Anyways, this is kind of tangential (and I'm not making an indictment of Mr. Coffey; forgive me for going so off-topic), but that's why I tend to be pessimistic when I hear recruits talk up how much they value "academics" in a school and how much advantage that should lend to schools like Stanford.