As a thought experiment, think of your own college experience. Do you really keep in touch with that many people? Of the people you do keep in touch with, can any of them open opportunities for you that are at all relevant to your field?
People who go to Harvard, Ivies, Stanford, Berkley, et al, have the same basic "College-Experience"(TM) as everyone else. No one wants to admit it, but it's not the network-effect that helps. It's the branding!
Harvard, the Ivies, et al, have brand recognition, and brand recognition helps...a lot!
If you're hiring someone, don't you think that the person with a brand that you recognize is going to at least get that person a phone-screen or an expedited interview? You're desperate to hire someone and they went to Stanford, so they must be good, right?
Ivy league degrees are simply the best door-openers out of all the door openers you can get. Once you're in the door they're as useless as the other degrees are.