Neanderthal and Human Interbreeding Puzzle

It's been determined that the Neanderthals and Homo sapiens in Europe did indeed interbreed. The first sapiens to migrate from Asia to Europe and establish a population there were the Cro-Magnon, who arrived around 30KYA. At this time the continent (and the entire planet) was warming, making life harder for the Neanderthals. They were too dense to swim in the melting rivers, not articulated properly to chase the new, smaller, faster prey animals who came along with the sapiens (as the ponderous woolly mammoths and other gigantic prey slowly became extinct), and with arm musculature wrongly shaped to use a bow and arrow.

Nonetheless, they did have their strengths, almost certainly resulting in the two species establishing relations and probably even living together. What clan wouldn't appreciate having a couple of big, strong, beefy guys to help fight off the predators?

The clincher is that the average modern European descended from the earlier Cro-Magnons (not the far more plentiful newcomers descended from the Indo-Europeans who arrived less than 10KYA when the Neanderthals were already extinct) has about 5% Neanderthal DNA.

The Basques, who appear to have no cultural, linguistic or genetic link to the modern Europeans (or any other modern people), may be the last surviving outpost of the Cro-Magnon, and they, too, have the Neanderthal markers.