The researcher who is usually cited for that claim (Rosalind Harding) claims she was misunderstood and/or misquoted. Her findings were that the red hair mutation was old enough that both types of humans were present at the time (Cro-Magnon and Neanderthal), and thus it could not be *determined* which population it originally arose in. The "popular press" of course grabbed onto the more sensational possibility and ran with it. But Harding herself doubts that it has a Neanderthal origin or that (as the media plays it) Neanderthals were necessarily all -- or even in part) -- red-haired.
Now for a good googling of Dr. Harding ... and if that's not inviting a law suit ...