This is a false implication, it’s possible that Neanderthal X chromosome just doesn’t “play nice” with human dna, and can’t result in fertile offspring. Admittedly I have not read the sources you recommend, so maybe they address this?
1. Neanderthal woman "Ann" mates with Human man "Hugh"
2. Ann gives birth to son "Ander", who is then raised with neanderthals. Notably, Ander has human Y chromosome via Hugh, but Neanderthal X chromosome via Ann.
3. Ander mates with human woman "Uma". They have a daughter, passing Neanderthal X chromosome into human population.
I realize this is a very specific path, but it would _only have to happen once_ for the neanderthal X chromosome to be introduced into the human genome. I think it is very unlikely that such a path would simply never happen across the thousands of interactions we had. And therefore I think the observed fact (no impact of neanderthal x chromosome in modern genes) can't _just_ be explained by the proposed behavior (neanderthal mothers raise their children in their neanderthal tribe)
I think there does actually have to be some sort of incompatibility, or some other very-very-high failure rate, something like 99.99%.
No, but it is an overconfident assertion.
Maybe all neanderthalis x sapiens were the results of rape. Maybe the fetuses were only viable from the n. sperm to s. eggs. Maybe something else.
All are possible.
What would be stronger evidence for an absence of neanderthal mothers among neanderthal/sapiens hybrid children would be a lack of neanderthal mitochondrial RNA in modern populations. This would point in the direction of no neanderthal grandmothers for us modern humans, though I'd be reluctant to present this as solid evidence. Maybe sapiens mitochondrial RNA is just better and there's selective pressure against neanderthal mitochondrial RNA.
None of this is to suggest that all neanderthal/sapiens couplings were loving affectionate parents. Just that the absence of neanderthal DNA on modern X chromosomes means nothing in this context.