Well, two factors here:
1) Counter-intuitively, getting into a prestigious grad school isn't quite as difficult as getting into a prestigious undergraduate university. Most of the top graduates from Harvard, Stanford, Chicago, etc. get top jobs after graduating from undergraduate and take themselves out of the pools. Also, many graduate programs are full-pay, which means that universities don't have as much of a problem with admitting students who aren't so deserving.
2) Chicago is a much more prestigious university than the people on CC or average college graduates think. The people at the top (who happen to be on the admissions panels at the top graduate schools) consider Chicago to be in the same league as Harvard, et al., and this is especially true for academia. In my job, where I interact with the most educated people in the international political scene, I haven't met a single person who hasn't pointed out that Chicago is a fantastic school after I mention that I went there.
As difficult as it is to believe, even after Chicago's increase in popularity for college admissions, Chicago's reputation among high school/college graduates is still MUCH lower than its reputation among employers and elites.