Earlier quoted context omitted.
You're still assuming that Vitamin D is involved in some interaction that itself is the cause of people being sick. Your reasoning is not allowing for the simpler possibility: sick people have less Vitamin D because sick people are too sick to go outside.
That's certainly a possibility, but we have two reasons to believe it's not true. One, even careful attempts to control confounders, still shows a substantial health benefit associated with higher sun exposure.[1] In other words, even among people with no discernible health conditions, the most sun exposed are healthier. Two, randomized control trials show improvements in biomarkers like blood pressure[2] and lipid p…
> As a measure of comorbid illness at the start of the study, we created a dummy variable ‘comorbidity’ identifying women who have been treated with antidiabetic [Anatomical Therapeutic Chemical Classification System (ATC) A:10] or anticoagulant (ATC B:01) drugs or medications for cardiovascular disease (ATC C:01–C:10) for more than 1 month.
This is extremely simple, hardly careful controlling. If anything it's a good example of bad science. Grabbed whatever was easily available in the database and claims they've adequately controlled for comorbidity while doing no such thing.
If you look at the difference in exercise, income, education and BMI there's a LOT going on between the two groups. You'd wish scientists would include the raw data and source code to easily calculate the adjustments yourself.