I think intelligence is kind of tangential to this.

A Degree means you could get through a lot of schooling. It means something. It means you can focus, you can learn, you can put up with some rules that don't necessarily make practical sense and still manage to come out on top.

It does take intelligence to get a degree, because you have to figure out all that crap and get through it. But the negative isn't true. Because somebody does pursue a degree, doesn't meant they are not intelligent.