I think it's probably a bit more complicated than that. The mutations that are associated with depigmentation (one study does seem to show actual causation) in modern Europeans might have arisen numerous times in human history. They, like other mutations, expand or "sweep" in populations, when they are highly beneficial. Studies done on SLC24A5, a major skin lightening gene, show that it seems to radiate out of the Caucasus in all directions. A few cases of SLC42A5 showed up in far northeastern Europe, but it may have appeared in other places as well.
So far, the scientific papers seem to be in agreement that the sweep of these genes to virtual fixation in modern Europeans may be tied to the effects of agriculture in Vitamin D poor climates. I have a hunch it may also be related to the consumption of milk products.
We also know that the studies of ancient Dna using the modern predictors developed for law enforcement show that Stuttgart was "fairer" than Loschbour and LaBrana. Otzi was probably "fairer" than all of them, because he had two copies of both the major skin depigmentation genes. The Neolithic farmers in Gamba et al were fairer than the presumably "Mesolithic" farmer, and this is also the culture (100% EEF genetically) where the oldest light haired, light eyed and fair skinned sample has been found.
So, it seems to me that the scientists may indeed be on to something.
It should be remembered however, that it's possible that Mesolithic Europeans had some totally unknown skin lightening snps, and the new groups introduced a totally new set. However, I think that's highly unlikely given the extreme rapidity in evolutionary terms with which these snps spread in more northern populations, relatively speaking. I think the most logical explanation is that these snps must have provided some sort of extreme advantage in certain areas, particularly during the transition to farming perhaps, so it seems unlikely to me that they were "duplicates" so to speak.
Speaking on just a personal level, I find it both ironic and sad that something which especially in the last couple of centuries has been the cause of so much suffering and discord should come down to an adaptation to climate and diet.
Oh, and thanks for the link. Very interesting.