Under subheading 2.2: "All residents in the nursing-home receive chronic vitamin D supplementation with regular maintenance boluses (single oral dose of 80,000 IU vitamin D3 every 2–3 months),"
The comparator (not recent supplement) group was on a different schedule, and had received a supplement probably two months ago.
>Finally, there were four total interventions: corticosteroids, hydroxychloroquine, "dedicated antibiotics" and the observation about Vitamin D. The more things you try, the less surprising it should be that there is a correlation along one of them.
Are you referring to these lines: "use of corticosteroids and/or hydroxychloroquine and/or antibiotics (i.e., azithromycin or rovamycin), and hospitalization for COVID-19 were used as potential confounders."
You only run up against ( https://xkcd.com/882/ ) when you perform multiple statistical tests, not when you merely have a heterogeneous study population. Unless they were also testing these other interventions, that critique does not apply.