I wonder if the prevalence of vitamin d deficiency is lower in lower in children and hence the lowered risk and transmission.
Further, among the adults who have a bad case of COVID-19, the vast majority had some relatively serious underlying condition (which is often correlated with age, but it seems to be the underlying condition, rather than the age, that is a better predictor of bad outcomes).
Additionally: there are many countries in which D-fortified milk (and even milk consumption among kids) is not nearly as common as in the US, but the age distribution of bad COVID outcomes seems to not change.
This is anecdata though, so it doesn't really mean anything.
Robert Gallo presented  an interesting idea to keep the innate system boosted by taking extra doses of a vaccine (he proposes using OPV). My pet corollary to Gallo's idea is that kids may have extended protection by having been more recently vaccinated (than adults).
Nature must have no professional editors on staff. What's the point of paying to publish there if you don't get the professional services? And what the hell are they doing?
Just publish somewhere that has always made all papers free to access and publish. Especially for COVID-19 research. We've always needed better and it's just painfully obvious now.
But your criticism doesn't necessarily check out as the average BMI of group B was actually lower than that of group A.
See page 4 of the PDF .
People have known about this correlation for months now. If it were really a thing, clinicians would be publishing case studies like crazy of successful treatment with vitamin-D. I'm not seeing that in the literature... so I doubt it will pan out.
That's why the MATH+ protocol  recommends Calcifediol or Cholecalciferol. According to their own review  the protocol reduces hospital mortality from 20-30% to about 5%.