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This would mean we should expect positivity and vitamin d levels to correlate. The study found reverse correlation.

I can see how it's confusing, but no.

If the type of person to take Vitamin D comes in for a test with less symptoms "just in case", then the probability that they are positive given that they are tested is lower.

Oh you’re right. I didn’t think carefully enough. Thanks! This does seem like a major factor to tease out.

No, if it's true, then it means that people taking taking vitamin D are more geared towards preventative measures, so they are more likely to get tested when in the absence of symptoms. More people who don't need to get tested would result in more negative test, so the inverse correlation is still the expects result.

Yes: There's evidence that lower-incomes are associated with less use of vitamin supplements [0]. And higher incomes would correlate to higher levels of health-care coverage that would allow for "just in case" testing.

[0] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2843812/

^ I think this is potentially the largest lurking variable here.