In the case of a graduate of a third, or even second, tier law school, I would want to see an even more impressive set of achievements demonstrating first rate ability before I even considered nominating him or her for a top tier court.
Your post suggests that you think the top tier law schools students are no brighter, just wealthier, better connected, more focused and with family values more conducive to aiming high, than the students at third tier and below law schools. That may have been true 40 years ago. It wasn't true when I went to law school 25 years ago and it's not true today. All you have to do is look at the LSAT scores and undergraduate records of the entering classes at the various schools.
In fact, students at lower tier schools may well be more focused and motivated to do well than the kids at the top tier, but they're looking for different things, typically. They want to learn specifically what they will need to practice -- a healthy attitude in many ways -- and are often older and come to legal education after several years working. The education itself at the top tier schools is pitched differently, it's more theoretical and less practical. It is geared more to training legal scholars, those who will end up teaching or writing about the law. In fact, the top tier schools are often criticized on that ground by practioners. However, when I'm looking for a first rate conservative legal mind for a judgeship, I would rather they have that training than the more practical, bar passage-oriented training at the lower tiers of law schools.