I smell BS. He suggests that these people around the coast gave up eating fish in favour of grains. I doubt it. Even today fish and shellfish feature heavily in the region's cuisine.
On the contrary this explains nicely how Sami people can be darker than Germans. They lived of reindeer, bird trapping and fishing, even like hundred years ago. It explains why Finnish are somewhat darker than swedes, we relied on hunting and fishing far longer than Swedes did.
He did not say that at all.
He said that there was the well-documented introduction of a new (convenient and scalable) source of sustainable food, grains. But now the people there are no longer surviving on a Vitamin D-rich source. Thus, their skin adapts to accept the only other source of vitamin D, UV from sunlight.
Also, it is important to note the scale of the changes. He is talking purely about change relative to other Europeans at the time, not Equatorial or even North African skin tone direct to blonde and blue-eyed...
In my opinion, a little bit more historical evidence from Scandinvian food scientists and census data, especially in the last XX years of globalisation should indicate whether this hypothesis is consistent with food changes and other trends.