Well, after I posed the question, I then noticed that you had about another 20 posts on the topic. :) Is it not possible however that a few Cro Magnon women raised mixed offspring, maybe as a curiosity, or out of the maternal instinct, or whatever, and the issue of the mixed offspring kept breeding with Cro Magnons, so the Neanderthal genes got diluted down to infinitesimal levels. That scenario of possibly some Neanderthal genetic material being in humans is the most likely to resist being swept away by the gathering genetic evidence, is it not?
And above, I do state that it may very well have happened on rare occasion, just not in such a way as to be of any consequence. I do not pretend any of my comments are 100% type comments. But the assimilation hypothesis is not a 'once-in-a-blue-moon' scenario. The basic premise of the assimilation hypothesis is that Neanderthals and Cro-Magnon intermixed to such an extent that Neanderthals were subsumed into the Cro-Magnon population.