I vaguely recall there being DNA studies that prove this is not the case.
http://news.nationalgeographic.com/news/2003/05/0514_030514_neandertalDNA.html
"A team of geneticists from Italy and Spain compared the mitochondrial DNA (mtDNA) of two Cro-Magnons that were 23,000 and 25,000 years old respectively, four Neandertal specimens, 29,000 to 42,000 years old, and a large database of modern human mtDNA to shed some light on the issue."
"The authors found that the Cro-Magnon mtDNA fit well within the spectrum of genetic variation exhibited by modern Europeans, but differed sharply from that of the Neandertals. They conclude that it is unlikely that Neandertals contributed to the current European gene pool."
“The molecular stuff has been very important,” says Milford Wolpoff, an anthropology professor at the University of Michigan and a leading critic of the Out of Africa theory of human origins. “But in the end it has the same problem fossils have—the sample size is very small.” Earlier this month, the journal Science published a Wolpoff study of early human skulls, which suggests that Africans may have mixed with earlier hominids rather than supplanting them. The small number of living humans sampled by geneticists, Wolpoff says, and the effects of natural selection over the millennia, make it foolhardy to say with assurance that Out of Africa is right. The geneticists, for their part, readily admit that they need more samples, more markers, and more precise calculations. But they also say that even with today’s imperfect science, the DNA is right. And in places like India and China, where the fossil record is scanty, the genetic history will be the only history. “Genetics is moving so fast,” says Chris Stringer, a paleoanthropologist at the Natural History Museum in London. “It’s well ahead of the fossil and historical record.”
The Homo Heidelbergensis sample (this was to check for affinities between Neandertal and us folks) yielded fewer than 400 base pairs, out of a presumed 16,000+ originally in the mtDNA. The “study” was GIGO.
Not what the data shows. mtDNA is a girl thing. The data shows that Neanderthal women did not contribute their DNA to modern Europeans. It is likely a Cro-Magnon man/Neanderthal woman match would result in a baby with a head too big for her birth canal.
OTOH a Cro-Magnon woman/Neanderthal man match could easily result in a kid that is stronger than mom's people and smarter than dad's people.
Why do you suppose our propaganda is saturated with the depictions of the enemy as ape-men coming to get our wimin?
It speaks to something very deep in the human psyche...