I think this is generally true (and I can't comment on the football player stuff), but I've had a lot of family and friends go off to the Ivies and comparable schools as well. Some of them are doing well, some struggled for a long time (or are still struggling). One of my brothers has a JD from Harvard and an MA in economics from Yale. He struggled for a LONG time to find employment. To be fair, the legal job market was a train wreck at the time, but still... You'd think that résumé would open some pretty fancy doors, but it seems like it hasn't. And even now, he's definitely not on society's "upper crust."
My other brother went to Duke and got his JD from NYU (shout out to my sister for keeping me from being the family "fuck up"). He'd definitely be considered part the "jet set" you described, but he also gets worked like an animal and I don't know that the connections he made at Duke and NYU really helped him all that much. I also don't see much point in having money if you never really get to enjoy it and you're going to have a heart attack or stroke and drop dead in the office before your 50th birthday.
I have other friends who've gone to Harvard, Yale, Stanford, Duke, Columbia, Brown, etc. and it's kind of a mixed bag. Some of them have senior positions at places like Blackrock and TOMS. Some of them are glorified administrators. Others are teachers at private and public schools. One of them works in a freaking chocolate factory (seriously). Ultimately, I think that your family background has something to do with it as well - especially within the Northeast prep school crowd.
On the other hand, a lot of my friends from UT went on to do crazy stuff. One is a very successful art dealer in London. Some are partners at places like Norton Rose Fulbright and Jackson Walker. Another is a very successful real estate developer (or something like that) in Hong Kong. Someone else is a professor at Cornell. And a couple of them are bartenders, substitute teachers, and middle managers.
That said, I agree with you - I love UT, but I would take an offer from one of the big three in a heartbeat. It definitely helps your odds, but a lot of what happens depends on how you handle your business. If you don't do the right things, you can still end up working in a chocolate factory...