I find the article a bit strange in some of its conclusions. Specifically the exchange of women. While I found one study in Nature that stated male hybrids may have been less fertile, and have seen other articles place this as yet unconfirmed by other studies and thus requiring further research, there is one thing we most definitely know about our genetic exchange with Neanderthal:
Their mitochondrial DNA does not survive in the homo sapiens populations. You receive 100% of your mitochondria from your mother. That Neanderthal DNA survived in our population, but their mitochondria do not, does not completely confirm hybrids born from female Neanderthals and male sapiens were inviable, infertile, or infertile of female. But it would certainly open a path to alternate explanations to consider why there is no sapien DNA found (currently), among Neanderthal populations.
Either way, I don't think you can just leave out the possibility that only hybrids with a sapien mother being viable. Or at least, not mention the lack of mitochondrial DNA possibly refuting the theories posed.
That said, this is just an interview. It might well be in the book. This is just what kept rattling around in my head whilst reading the article. And regardless, it is a fascinating subject, which every expert will agree we still have much to learn about.
This article, and book, really help to bring obviously problematic assumptions to light to those, like you, not obsessing on a particular theory and trying to look at the bigger picture.
One of the fascinating things eclipsed by the shear surprise and obsessing related to potential cross-species mating is that the shared neanderthal and denisovan DNA is wonderfully diverse in its levels, ratios and types depending upon what region a person is from. This indicates that hybridization occurred everywhere or, alternatively, we should consider that estimating a date and location of introgression would be problematic for populations of isolated migrators and so we should consider the relic DNA may be ancestral.
It is not ancestral to the neanderthal species itself, hence the lack of our DNA in them, but it is ancestral relic DNA left from intermediate species that still mingled during and after speciation creating a diversity of relic DNA for hominids whose survival niche was migration to greener lands in dry times. When Svante Paabo took the job at Max Plank part of his goal was to cultivate the public excitement about neanderthals. The theory of interbreeding in Europe seemed an easy-to-prove pursuit but it never happened and the time and place of interbreeding turned out to be elusive. What he may have found is evidence of a much more interesting theory to blindly obsess about, which is, the genetic record of a speciation event of a species that was isolated but much less isolated than neanderthal and that survived by maintaining alliances based in trade with distant tribes of our own species. Migrators cross breeding with intermediate species 150 to 250 thousand years ago may produce the same shared DNA we see today.
Ancestral DNA is driven out when a population is less isolated and this may be why the San and Yoruba tribes lack neanderthal DNA entirely and the far away migrators have more. The statistical analysis that supported potential times of interbreeding has changed so these models of genetic probability may not be as solid as many presume, and probably not reliable for isolated migrating populations existing alongside intermediate species that are more closely related to neanderthal.
Consider the Jebel Irhoud fossils in Morocco. Classified as modern humans but they have those long neanderthal skulls indicating speciation was still in progress 315,000 years ago and there were many hominid types long after our divergence with our last common ancestor with neanderthal.
The picture may come more into focus as we get more DNA from fossils like this.