Remember that the data suggests exactly 2 individuals dropped into human populations that were locally in the tens of thousandsI did not notice that, but it seems that's just what we have detected so far. If it can happen twice, isn't it very likely it would happen quite a few times?
As to species barriers, by definition a species is what is reproductively isolated.
Biology is not nearly as clean as say math, and so reproductive isolation is quite blurry.
Some times A + B works and B + C works but A and C are reproductively isolated.
Often, A + B makes, C and C + (C or A or B) makes D, but D is infertile. Or E is infertile. And while A + B makes C and even D and E, the fact that the lines eventually terminate means A and B are reproductively isolated.
The foals would be mostly horse, and the result of that is an animal that is 3/4 horse which therefore is likely to be able to breed with other horses.
Not so.
It is true that once in a million a fertile mule is born, but that mule's offspring are not fertile, or its grandchildren are not fertile. Mules have been bred throughout history, but I know of no line of mostly donkey or horse hybrids with a fertile mule parent, or gand, or grand-grand-grand parent, or any mule linage.
and by chance on 2 occasions fertile offspring
But that in no way guarantees THEIR offspring with either Humans or Neanderthals (or other hybrids) would be fertile or that their grandchildren would be.
And if they were, then by definition us and Neanderthals are the same species.
And in that case I still don't understand how there could be so little genetic difference contributed.
For sweet zombie jesus' sake, we can identify the descendants of a Central Asian male who lived around the time of Genghis Khan over most of Eurasia. And successful interbreeding with a population who lived apart for 200 THOUSAND freaking years leaves only a few stray genes?