The problem with the theory that interbreeding with Neanderthals made Eurasians smart is that the Neanderthals themselves were probably quite stupid (their brains were larger than ours because their bodies were more massive). Neanderthals were using exactly the same crude stone tools around the time they went extinct 40K years ago as when they originated some 400K years earlier. If Neanderthal genes gave us insightful, creative innovative minds, you'd think that Neanderthals would have had a little more creative insight of their own.
I suspect that a more likely explanation is that people in Africa coexisted and interbred with archaic Homo sapiens (aka H. heidelbergensis) for longer than those who left Africa.