You can't really know for sure, but the typical argument (c.f. Chomsky & Berwick) is there was an enormous explosion in "cultural" products then. Before then, we don't see figurative art, and after we see all sorts of crazy things.
Genetically is seems it's very unlikely there is a single gene spot that explains human language but a confluence of different factors feeding back into one another in linage we do not have genetic access to at this time. We've done a bit of gene testing around this now, and single gene flips aren't near enough. I think the best analogy would be like playing a video game where you have to flip a number of switched to the correct position to get the system to work together.
People really do flagrantly misrepresent his claims.