They were looking at antibody titer in those with vitamin D supplementation and those without.
Not only is that failing to test the claim (vitamin D blood levels above xyz nanogram/ml in the blood, have such and such vastly lower rate of hospitalization / death from coof)...
but it's kinda flawed since we have no way of doing contact tracing to see the amount of virus any one person has been exposed to, or when.
I think you are correct in the flaws of the study. I agree with you, however I think it does lend credence to vitamin D is not the sure fire prevention some think it is. I appreciate your critical and analytic look at the literature. There is much room for reasonable debate.