Well, Gates' mother and father may not have gotten together at all were it not for his father making something of himself with the help of the GI bill, so it's definitely somewhat involved. It's not clear from internet searching if William Gates I was wealthy or just had a pretentious approach to naming his kids, so it could be that he'd have gone to university anyway.

That said I wasn't trying to point to it as the sole contributing factor for Bill Gates, just one of many that may play a part in the overall trend and noting that one of the most obvious has it in his family's history.