I'm not convinced: Neandertals still might have interbred

The nail in the coffin of theory that Neandertals interbred with modern humans is typically the mitochondrial DNA which typically shows that Neandertals broke off of the human family tree prior to modern humans. We typically use 100,000 years as a demarcation for human, although in reality our ancestors have always been the same species as far as you go back even if that species is a type of fish or worm. Deciding when during an evolution to say this is a new species is an arbitrary point. Anyhow it seems on pretty good authority that Neandertals last shared a common ancestor with humans 660,000 years ago, so they certainly aren't an ancestor but a near cousin (in the same sense that the tree out my window is a distant cousin). Mitochondrial DNA (as you well know because you're smart (if not you will be)) is passed from mother to child along a material line all the way back to the mitochondrial eve (scientists need to stop calling shit Adam or Eve they make for really bad names).

Now this seems pretty clear that no genetic material was passed around between the neandertal population and the human population when the human population left Africa for Europe, right? Well, I'm not convinced. Neandertals were strong, really strong, Arnold Schwarzenegger Mr. Universe strong and this holds true for the women as well. In order to get our mitochondrial DNA to show signs of Neandertal interbreeding we need to posit that a man had sex with a fairly ugly brow face woman capable of breaking him in half and that from that union somehow the kid got taken care of from the human side (even though mommy would raise him) and that from that there is a *direct* maternal line going back at least 15,000 years and these one of these individuals wasn't picked up by a small sampling of the human population.

1) Neandertal men + human women = much more likely.
2) Sample size might be too small to find mRNA traces within human population.
3) The traces might have just been lost.

I don't mean this to sound like special pleading by any extent, rather I just don't find mitochondrial DNA to be a nail in the coffin. We really might have had plenty of interbreding with the local population and bear no signs within our mitochondrial DNA.