The linked study (which was an abstract) has been taken off the link for good reason. At any rate, I am thoroughly familiar with the pre-print. I only quote 3 comments to the pre-print page that, in my opinion, summarize the principal reasons why this is, medically speaking, a totally worthless publication, which cannot allow any conclusions to be drawn.

Before accusing specialists of "scientific arrogance", one should be held to the same standard of scientific competence.

This does not mean, of course, that the medical establishment does not lie, obfuscate, collaborate with fascist police-state measures, corruptly disappear valid data and promote more profitable but totally worthless recommendations. It certainly does a lot of that and has lost the right to anyone's respect if it ever had any. But that's still not a valid reason for pushing quackery.
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Below are 3 readers' comments selected to summarize the main reasons why the quoted study, or at least the medical pre-print paper referenced, is worthless:

Atle Fretheim • 4 days ago
These are interesting results, it they're valid. Unfortunately there's no way of telling if these results are believable, since the manuscript contains no information at all about the randomisation and alloacation procedure - as far as I can see. The authors should provide a detailed description, in line with the CONSORT statement (http://www.consort-statemen...). And since research findings travel very fast these days, the authors should do this right away.

Jon Lundberg • 3 days ago
There is no placebo. In my view its unetchical even to do a studly like this, how on earth is it possible not to include a placebo and make the study randomised and double blinded?

Dr. Julian Keogh • 4 days ago
Although the paper claims it is a randomised study, it also says that all patients treated in 5 wards received calcifediol treatment, while all three of the other wards received no calcifediol. How this study can be considered randomised is therefore questionable (maybe the wards were randomised but that is a very poor level of randomisation). It is also presumably open label, meaning that the attending physicians and decision makers would have been well aware whether the patients were receiving calcifediol or not.[continues with several other invalidating points]

Replies: @Thomasina, @just-a-name, @mike99588, @paranoid goy, @Fox, @DrWatson