They probably had to take a guess, to conclude the show. Though the National Geographic Society is not even a scientific group.
All in all they are entertaining. Neadertals is an interesting subject to me. I would guess that they were part of the Ice Age Mega Fauna (well they had some big hominid features sorta) that could not adapt fast enough to the warming climate after the last Ice Age. They probably were in decline from the climate, and were out competeted by the more adaptable
Homo sapiens sapiens. Had the world remained cool I think they would have survied in isolated populations, in areas where thier prey survived.