The curious total lack of any evidence of interbreeding between modern humans and neanderthals is most problematical precisely in the levant in which moderns and neanderthals are known to have existed in close proximity for long periods of time and you'd figure interbreeding should have been very common IF it was possible. A curious statement. "The Levant" is exactly where the intergrading of human and Neanderthal features is most pronounced. Note the comments on the linked page regarding "Skhul V" specimen in particular. Then there's the Lagar Velho child from Portugal, which looks a lot like a human-neanderthal hybrid.
Aside from the fact that you can't make any sort of a case based on one or two skeletons, the fact that the one or two possible crossbreeds for which somebody does have skeletal remains did not live past childhood might tell you something. As I see it, the preponderence of evidence including the DNA studies, Shreeve's article, and Gunnar Heinsohn's comments indicate that neanderthals were the human type antecedant to us, and that the changeover was rapid and driven by design change of some sort rather than evolution. That doesn't preclude the two types living in proximity for some number of generations AFTER the introduction of modern humans.
That apelike rib cage is a real kicker. That's a piece of the puzzle I was not aware of until now. That alone would probably make a neanderthal so ugly to one of ourselves as to preclude dating or anything like that.