There's a very large gap between your first two sentences, especially since it's quite common for there to be large variations in intelligence among people raised/educated in similar environments.
I'm not maintaining there is no genetic effect. I see plenty of indicators around me pointing both ways. I think it's a mix of things. I wished someone would have pointed out Plato's writing to me when I was a kid. It would have accelerated my intellectual development tremendously.
At the same time, there's a tendency for people of similar environments to have higher intelligence of people in other environments (the achievement gap).