Most of these studies suck. For example, as mentioned in this response, https://academic.oup.com/jcem/article/106/12/e5271/6348963, to that first linked study (which may apply equally to the second, as it was just a trial for the subsequent study):

> However, the authors did not provide information on 25OHD serum levels after the supplementation, limiting the evidence of a causal link between vitamin D supplementation and the observed clinical outcomes.

IIRC, there was a similar study to the above that was retracted, in fact. Possibly even #2 above?