@cray74 - You did say, "why didn't we bring Neanderthal girls home to meet mom and dad?", which I took to be a way of saying "we didn't interbreed with the Neanderthal girls", was I wrong? What did you mean?
Yes, I was wrong about the mitochondrial DNA… I was confusing the date of MRCA (about 3000 years) and the matrilineal most recent common ancestor (mitochondrial Eve, about 100,000 years).
I'm not sure how the statistics play out… I wasn't suggesting that a single avalanche would destroy all Neanderthal mitochondrial DNA descendants in a single event, but that the total hominid population at the time was small, split into related groups, and random events in small samples easily give extreme results. How often do you roll three avalanches on three dice, or two avalanches and a mammoth stampede? I'd like more evidence before saying the "blitzkrieg" scenario is the most likely.
So, another possibility, as you hint, there could still be living groups with Neanderthal mitochondrial DNA that haven't been sampled by a passing geneticist. Ah, Vociferous seems to be proving us both wrong :-)