This is a nice example of the slipperiness I sometimes notice when I think about how one could test an ev. psych hypothesis. My first thought after reading your comment was 'but won't all those factors be just as correlated with unhappiness and depression as with genetic fitness? Surely there's a less complex explanation here: unhappy people don't like living as much, so they try killing themselves more.'

Then I thought a little more and realized that could also have an ev. psych basis: maybe we evolved to kill ourselves more when we're unhappy with life. But that's a different ev. psych argument than 'we evolved to kill ourselves more when we have low genetic fitness.' Or is it? Maybe we evolved to kill ourselves more when we're unhappy because unhappiness correlates with low genetic fitness? What would it even mean in concrete terms for all of these possible evolutionary explanations to be false?