I think most of what you say is pretty much correct.
One little point to remember is the "Cro Magnons" are fully modern humans. In that sense they are "us".
Now if there was interbreeding between fully modern humans and Neandertals then that would tend to support the view that Neandertals should be classified as a subspecies (interfertility is an important consideration in such comparisons even if it is not the only consideration). That does not invalidate the DNA analysis, it is just another factor to consider when making a decision on the taxonomic classification.
I seem to remember some criticisms of the methodology of the mitochondrial DNA studies on this forum. Does anyone else remember any more details ?