If suicidal thoughts are considered a health-status, then this whole study is pointless, because they're controlling for the thing which directly leads to suicide. Perhaps I'm misunderstanding your point?

One other commenters gave a really good one, people who fill out subscriptions are less likely to have committed suicide because they still care about staying alive enough to take care of themselves. Suicide is a damn complicated subject, but if one is considering it, making the effort of filling a prescription seems... pointless, and I think if we look at people who fill out any non-psychoactive drug vs. committing suicide, we'd see a similar correlation. (Psychoactive excluded because things like depression meds are specifically meant to reduce suicide risk factors, and I believe would confound any results)

Unfortunately no, this is an observational study, not an experiment, so even strong correlations are just correlations.