I know two really chill people that went to Stanford, and only one pretentious D-Bag. But, I met them when they were in their 30's or 40's. So maybe it wears off after a decade or so.
Two of the most humble people I have met are PhD's from MIT. I worked with both of them for years before someone told me about their amazing credentials. I said something about how smart each person seemed, and another coworker said, "Yeah, no sh!t. He's got a PhD from MIT."
Unfortunately, the loud mouth that brags about his degree from Stanford holds the highest job title among them all. There is something to be said for self-promotion if you want to climb the corporate ladder faster.