It doesn't follow that if human males stole Neanderthal wives sometime in the past, that you would necessarily see Neanderthal mitochondrial DNA in present populations.

Consider a serial 'wife-stealing' human culture. One generation of human males leaps upon a small population of Neanderthals, killing the men and stealing the women. The next generation, a new group of half-neanderthal males leaves the colony in search of wives, finds a human group, kills the men, and steals the women. The children of this generation will be 1/4 Neanderthal with no Neanderthal mitochondrial DNA. Imagine that the first colony gets wiped out, as most ancient communities were. There you go.