"It's a Bayesian problem"
This we agree on. But we have to factor in adverse selection. If you're a prestigious employer, adverse selection is going to be small to non existent. The Harvard grads joining Dropbox are going to be all excellent. If you're a tier-2 employer with no particular unique value proposition, a Harvard grad that is willing to join you isn't the same thing as a randomly selected Harvard grad (unless there's a compelling reason why they would want to join), let alone the same thing as a Harvard grad entering Dropbox. There are selection effects working against you as an employer.
I've seen this personally, working at a little known company in a traditional industry without much to offer, we hired a Princeton grad who we eventually found out was fired from a few places and turned out to be worse than useless. We got adversely selected. They only wanted to join us (instead of a "better" company) because they were the bottom 10 percent of their cohort (not necessarily in terms of GPA, but in terms of ability to make themselves useful).
Useless people from Ivies are rare, but they do exist, and if you're an employer facing adverse selection you become much more likely to end up with one of those.
(Actually, I've worked with useless people from Cambridge, Tsinghua, and a few other elite colleges, many of whom we had to fire. The common theme was that they couldn't get into a better company, and so they joined us)