"It is difficult to tell if this is an indication that YC overwhelmingly prefers people from extremely prestigious name-brand universities, or only people from said universities have any chance of being "connected" enough to get into YC."Neither. In our class (S12), there were founders from every background imaginable. I also know founders from other classes, and the same is true amongst that sample. If anything, YC founders seem a bit less "credentialed" than the Valley in general.
To the extent that "name-brand" universities tend to graduate extremely smart, capable people, you'll find that they're over-represented in any sample of smart, capable people. But YC has no incentive to select for factors that don't correlate with outcome.