They have looked at mtDNA sequences in Neanderthal fossils and early human European fossils and the sequences characteristic of Neanderthal fossils are absent from the early human fossils that they've examined. That is powerful evidence of no intermixing, at least so far as the bloodlines of those particular early humans.
Maybe I just need a little more coffee, but I'm still wondering about this mtDNA conclusion.
Let's say we have ten generations of females, mother-daughter-daughter...
The first mother in the sequence is pure-CM. She mates with a pure Neandertal and so does every female down the line. (I know, just a thought experiment.)
The tenth lady has mtDNA telling us she's CM. She looks like a Neandertal, as she jolly well ought after all those Neandertal male ancestors.
My question is, are we looking at anything besides her mtDNA? And is mtDNA by itself, in a case like hers, telling us what we need to know? In other words is it giving us truth or just fact?