They have found that modern humans share 1 to 4% of their DNA with Neanderthals. Present-day Africans do not have Neanderthal DNA. This suggests to me that breeding with Neanderthals is responsible for a fair amount of the diversity of human morphology, including red hair and fair skin.
Another recent discovery : redheads have different pain pathways. They are less sensitive to pain, and less susceptible to pain blockers. There's something genetic there, and my hypothesis is that it's in those Neanderthal-introduced genes.
Also, the redhead at the top of the Gizmodo article bears a passing resemblance to Wilma, the Neanderthal model.