It likely is that people who have issues are more likely to try changes from the normal in a hope that will help the issue. That said change may have no effect on the issue doesn't matter. For example at my church's eatin' meetin' today after the service, there was one person who mentioned going on a gluten-free diet in case that would help her digestive problems. This despite not having been tested for gluten intolerance and hearing from another member that he's tried the same a while ago to no effect.
Since vegetarian is non-normal in our society, it's not surprising that people with mental health issues are more likely to be vegetarian.
Incidentally, I went vegetarian for Lent last year. It helped that Sundays are not part of Lent, as the only real problem I had with it was when I was dining with friends and family.
That sounds like something right out of ODF's playbook, but he finds far more excuses than just one.