In some ways it isn't the most important thing in this situation, but in others it's representative of the entitlement that certain elites feel by virtue of their backgrounds and institutional affiliations. Sure attending an elite school represents genuine achievement for some and confers genuine benefits to most, though more of the networking and credentialing kind than the education kind, but the belief by some (many? most?) of the people who attended college in "Boston" that their classmates are truly the cream of the crop, and not just in average sense but in an almost universal sense, as if the worst Harvard grad is superior to the top grad of the next best school, would be hilarious if it wasn't so damning of the whole lot of them.
I doubt anyone actually quite would say they believe that, if pressed, but the way that academic hierarchies are so ingrained in the people who benefit from them, there's a tendency to act as if they do. You know, the Harvard job/grad school applications go to the top of the pile. And whatever relative "quality" of the median Harvard grad in certain ways (recognizing how we think about this stuff is very limited in scope), or the top quintile, or whatever, there are a hell of a lot of lazy dumbasses running around Harvard (and every university). One way to understand this is knowing that at elite private schools the gentleman's C (which is really a gentlemen's B- at most these days) is the gentleman's F at a typical state university. There might be some majors where this is not quite true - you can probably only get so far behind as a math major without at least being encouraged to pursue other interests - but in general if you at least show some modest interest in fixing your failures, that semester you blew off will turn into an incomplete which will turn into that gentleman's C. At my state school, people just failed out.
Anyway, the idea that attending any of these schools is proof of much of anything other than doing the right thing (often with significant help from your prep school) at one particular moment in your life (ages 15-16) is ridiculous, and that's before we get to legacy bonus points.