This seems somewhat true based on spikes in the Southern US during the summer (people stay inside where there is AC), but doesn't seem to be the whole story. If that was the case, you would expect to see similar spikes in areas where there is say a week of rain (should be easy to measure in parts of Europe).
In my country - where for the last month we've basically had no sun, just clouds - there is a distinct spike around winter, which would follow nicely with the vitamin D theory. However in places like Southern Europe, which still has a good amount of sun during winter, there are similar spikes.