I know and work with a fair number of people from CalTech.
When new grad students - who come from other universities - are first prepping for doing their teaching / support of the CalTech undergrads, they’re told flat out: they aren’t nearly as smart as the kids they’re going to teach.
This breeds a lot of arrogance, of course, even if it may be true in most cases.
The other thing about CalTechers is that so many undergrads burn out by senior year. Many don’t go on to do great things in private industry or further higher-ed like they’re supposed to, and instead take a number of years off to try to recover from the experience.
But... but... WHAT ABOUT HARVAAAAAAAAAARD?!?!?!