Doesn’t inbreeding imply a lack of intelligence?
Do you think that holds for the crowned heads of Europe, England, and Russia? Hmm. George III; crazy, but not stupid.
Interbreeding not inbreeding.
In other words they bred with the other humans that immigrated into Europe.
But there were a lot less Natives then immigrants. So the end result was like a drop of ink in a gallon of milk. They were diluted and spread out.
The fact that a male Neanderthal/female Cro-Magnon would have probably resulted in the female and probably baby dying while male Cro-Magnon/female Neanderthal would have resulted in a live birth and live female would not help to keep the Neanderthal culture alive.
Inbreeding implies lack of opportunity, and distance between groups. This was one reason why esquimos allowed traveling hunters to have sex with their women as guests. Get some new blood into the tribe. Also, avoid conflict. Here is a link to new thoughts on the parenting behavior of Neanderthals.
http://www.insidescience.org/content/cuddly-neanderthals-parenting-skills/1623