I have read about links between Vit D and several autoimmune diseases. The recurring theme seems to be the level of Vit D received by the mother, while pregnant and then the child until they reach about 15 years. Have linked to the studies on this forum before.
I'm neither convinced, nor unconvinced, but I am sure of a few things:
A lot of people are not getting enough Vit D
As Vit D deficiency has been studied in more depth in recent years, it has become clear that it is connected to many more cell functions and immune functions than were previously realised.
There has been a rise of autoimmune diseases during the period when Vit D deficiency has worsened.
Correlation does not prove causation, but they are finding more evidence all the time.
I was tested for Vit D deficiency with several of the symptoms, supplemented, the symptoms disappeared, and I now feel a great deal better.
The body needs Vit K2 simultaneously with D3, in order to get the best benefit from supplementation.
This is the best introduction to the subject that I have yet found. This guy's references are always good. And he gives much better quality info than the link in the OP, which seems like a sales pitch/miracle cure suggestion.