HN health posts tend to get posted without context and you'll get a pile of people [inadvertantly, I'm sure] pushing their supplement regime as a way to stave off clinical depression et al. This paper is NOT saying that low VitD causes psychiatric admission, just that patients may require supplements to bring them back to healthy levels. You get most of your vitamin D from skin exposure to sunlight so it's reasonable…
I wouldn't say people are necessarily "pushing" their personal regimes, more often than not people are merely exchanging their personal experiences with certain issues.
Personally, I've had actual relief from a really annoying issue (nightly teeth gnashing) thanks to a helpful HN comment pointing me in the direction of Magnesium. I'm still thankful and glad that happened!
Btw: The headline is spot on with what the study found. I don't get what you are suggesting there with "reasonable to suggest that these people with psychiatric issues and low VitD are likely to be shut-ins".
Only 8.7% of all patients were vitamin D sufficient at admission. They didn't get their insufficiency from being admitted, they already usually have it when getting there.