Of course he doesn't build rockets. Logically no one builds rockets. Yet somehow without him SpaceX rockets wouldn't get built. What are the number of individuals at SpaceX that we can say, "Without that exact person the company would not work?"
I'm not saying it's absolutely the case that he's the only person who answers that question but I would say that the number of people who do is a number somewhere between one and something very small. I'm also saying that he's in that group of people.
Unless PhDs are awarded to people who dropped out after two days, that didn't happen: https://en.wikipedia.org/wiki/Elon_Musk#Education