Yes, but in Templeton's analysis he does not find evidence that the Neanderthals were assimilated. He states explicitly that their status is "indecisive". So, in light of the mtDNA research, I still think the balance of the weight is against Neanderthal assimilation. Though point well taken about the multiregional hypothesis!
You can't use mtDNA to prove you're related to your father. Mungo Man, a "modern" human, also has an extinct mtDNA line.
mtDNA is better evidence when it shows something positively than when it fails to show something.