But I don't have a dog in that race: if you are skeptical, great -- find the holes in the case. Why is this a failing on my part? What does this have to do with me?

I'm not out after holes. I'm interested and I want to learn more about this. But I haven't found anyone arguing for this theory that you say exists. I keep asking for evidence because I haven't seen any. All the paleoanthropological evidence that I've heard of shows that Neanderthals may well have had customs, abilities, or understanding comparable to those of humans, so they weren't any less intelligent. I haven't been able to find any suggestions that they were more intelligent than humans.