I am an archaeologist and I must diagree from a professional viewpoint. While my specialty is eastern native American ethnobotany, not neaderthals. I believe the jury is still out on the subject. The DNA studies from what I have read on the subject have been far to small to be a definitive sample.
The evidence is not definitive, but what evidence there is points toward no interbreeding. There is certainly enough evidence to declare that the headline of this article is false. By all appearances, we did not sleep with Neanderthals (even if we did). It is not 'appearances' that makes people such as this lady imagine that we did; it is nothing but merely their fantasies about how Paleolithic hominid populations in Europe 'must' have behaved..