This article mentions, but fails to highlight, a very important point:
"We found a variant of MC1R in Neanderthals which is NOT PRESENT in modern humans, but which causes an effect on the hair similar to that seen in modern redheads." (my emphasis)
There is no more a link between the modern ginger gene and the neanderthal ginger gene than there is between the blue-eyed gene in dogs and the blue-eyed gene in humans.
The Reg's slow descent into the depths of inaccuracy carries on apace though.
From the article:
"Researchers from the University of Barcelona identified a mutation on the gene MC1R that, in modern humans, causes hair to tend to the titian, and skin to tend to the pale. All humans carry a version of MC1R, but the redhead version is slightly different, the BBC reports."
This genetic variant does not exist "in modern humans". It has been artificially introduced into tissue cell cultures in a lab.
Your tag "Similar to modern humans" is sooooooooo misleading. It implies that the gene is similar, when it is not -- it is only the effect of the gene that's similar.