I think they are presuming the rest of the genome is pretty much identical.
Wait until they get into epigenetics ~ that's where you'll find the Neanderthal materials all over the place. After all, a mere 20,000 years of contact with life in the midst of an Ice Age is really not enough to elicit the sort of cold climate adaptations modern Northern hemispheric humans exhibit. On the other hand, a full 400,000 years of such contact, as Neanderthals, ought to explain it all quite readily.
I like your hypothesis. Given an "out of Africa" human population encountering a Neanderthal population, some amount of interbreeding would have occurred. It now seems that hybrids were viable. A hybrid African/Neanderthal might have been better able to survive in temperate-to-cold climates than either pure African or pure Neanderthal, and so the population with the right mix of Neanderthal genes would have spread.