If there's one thing poor kids have, it's free time. I think it's actually relatively easy for a smart poor kid in the US to learn ~whatever they want; that was certainly my experience, and I think the structures that were available to me are available to basically any American kid today.
One thing to keep in mind is that poverty is strongly anticorrelated with intelligence - this is not PC, but the evidence is overwhelmingly clear - so it's easy to see that there aren't many poor kids doing stuff like this and (mistakenly) conclude that it's because they don't have the extrinsic opportunity, rather than that they lack the intrinsic means.