the correct model is not "early programming causes great programmers", but rather "X causes great programmers, and X causes early programming; therefore early programming correlates with great programmers".

Yeah, I think this is explicitly the claim Paul Graham made, with X = "deep interest in technology".

The problem with that is I think, at least with technology companies, the people who are really good technology founders have a genuine deep interest in technology. In fact, I've heard startups say that they did not like to hire people who had only started programming when they became CS majors in college. If someone was going to be really good at programming they would have found it on their own. Then if you go look at the bios of successful founders this is invariably the case, they were all hacking on computers at age 13.