Yeah, this is a crucial point. This is studying "adults with suboptimal baseline." If you have a vitamin deficiency and get sick, I would expect supplementation with that vitamin to provide some relief, regardless of which vitamin it is.

This does not mean that the same will happen for people who did not have a deficiency.

Having said that, there is good evidence that Vitamin D deficiency is widespread, and supplementation of Vitamin D is relatively safe unless you take excessive amounts.