Somewhat coincidentally I am reading "The Language Puzzle" and the author puts forward the theory that based on the tool evidence left behind that the language development of Neanderthals was as much as they could do with their brain physiology and environment, i.e. there was no improvement in stone tools over their entire history versus the other human population evidence we have at close to the same time and that the improvement in stone tools in other populations had to be verbally communicated. There of course is the bias in the evidence we have may not be fully representative and this theory is not mutually exclusive with the genetic argument in the article.