No, of course it has nothing directly to do with occupation or degrees. But there is a genetic component to intelligence. If the parents are definitely both very smart people, there is a higher chance that their child will be bright than if the parents are just two random people.
I have never heard anything about Clinton's SAT scores, but there is no question he is very smart even though he may be morally lacking. People who have known him agree that he can absorb new information much more quickly than most people. Kenneth Starr himself said he wished he was as smart as Clinton.
In a place like Princeton there are people with more average intelligence and some who are among the smartest people that exist. If someone has two parents from the latter group, they could turn out to be an idiot, but it is less likely.
First, the genetics of intelligence are very complex. We don’t even understand the genetics of high blood pressure, let alone intelligence. It’s not like eye color, hair color, or blood type. The correlation is essentially non-existent. Ability in specific areas of thought likely involves many genes, and polygenic traits can skip many generations.
Second, Bill Clinton is not a very impressive intellect, similar to most politicians.
Third, Princeton’s most famous son, Einstein, didn’t go to Princeton, and was a late bloomer. He worked as a third class patent clerk at the Swiss patent office in Bern, but pursued his science in his time away from the job. He could only do this because his science was theoretical and not bench experimentation based - which would have required him to have a lab and funding. Thankfully, he had the opportunity to pursue his interests thinking outside of the box. If he had been part of the general system in science that exists today, his ideas would likely not have been listened to, as he didn’t have the proper pedigree.
The point is that pedigree is an absolute, unequivocal, JOKE, and has been responsible in large measure for much of the suffering in the modern world. Don’t buy into that tripe.