From what I gather this found only some correlation, not causation. So I might as well postulate that people with mental health problems are more likely to be on social media. That's not too difficult to believe.
But you're right insofar as this doesn't appear to be a longitudinal study with a control group. But such a study would probably be pretty hard to pull off.
Maybe ESS[1] could help here if questions about social media habits were added - but we'd not see results until a few years hence, obviously.