You're refuting his view as rosy, but positing that the real answer was horror. It's almost certainly something in between the two.

Personally, I think that the most likely explanation is that most mixing came through adoption of fertile women into the human tribes. Males of other tribes would probably not have been accepted so readily, and likely driven off or killed, but fertile females would have been more easily integrated. From there, you naturally get a mix of the two.

The relative percentages of Neanderthal and Sapien DNA in modern humans would indicate that Sapiens outcompeted the Neanderthals and relatively few interbred with us.