Honestly, I am not sure why this study is noteworthy. As you pointed you, the evidence is weak. Plus, we have the results of a good randomized controlled experiment. I don't think we need anything more to make up our mind (yes, vitamin D3 works very, very well): https://www.sciencedirect.com/science/article/pii/S096007602...

Note: The study link is for treatment, not prevention.