We seem to be having different conversations. I'm responding to

  if we know for sure the genes are the same and nature is off the table, how much variance remains?

For intelligence? Where "nature" refers to "innateness" of the trait? I think it mostly is off the table, yes. I'm not saying that the only or even the most important environmental trait is nutrition.

(I think it can't possibly be entirely off the table, since we have mechanistic understanding of some gene-mediated cognitive disabilities).