The sources linked above claim that some can be taught, and some (probably most of the population) can't, no matter what you do. And of those who can learn, many become autodidacts in a suitable environment.

Of course they don't reinvent programming themselves, they do learn it from others, but the same could be said of any skill or knowledge. And yet there are skills which clearly have very strong inborn dispositions. It's being claimed that programming is such a skill, and an extreme one at that, with a sharply bimodal distribution.