Tequila Sunrise
Adventurer
I find this easy to believe. Since first replying to this thread, I've thought back on my gaming history. Here's what I've seen:Mental health is, even in the 21st century, a rather taboo topic. You may not think you know many mentally ill people. However, the statistical likelihood is that you know many.
Grade-school friend who taught me D&D: Crazy smart. Played the game with me for about a month, then got bored and moved on to a new hobby. (This was common for him.) Despite having a ton of friends, he suffered acute social anxiety and a hyper-active mind. (He got A's without trying.) As an eventual result, he got heavy into drugs in high school and is currently off the map. (His parents don't know where he is, and are bracing for some police station to call and tell them that he's dead.)
College gamers: One was bipolar. Another made me realize that I needed a "Don't show up drunk and/or stoned" rule. Another miscarried at one point, and was pretty depressed after that.
NYC gamers: I briefly gamed with a couple who were uncomfortably happy. It was weird, almost Stepford Wives weird. There was some kind of craziness going on there. Aside from that couple, most of the NYC gamers I played with were mentally sound...aside from the pervasive New Yorker craziness. (I swear there is something in the water...and I'm going back in September!)

Rural gamers: There was the autistic kid I had to kick out after he started threatening me. His sister was a good friend of mine, but pretty depressed. And one of the gamers I've known longest 'round these parts is a furry, but I'm not sure that counts as mentally ill. (Life's tough for him, but if he's not hurting anyone or anything...?)
And then there's me; for a good three or four years, I was pretty depressed myself. Not "I put a shotgun in my mouth every morning and think about pulling the trigger" depressed, but enough that looking back now, I don't know how I didn't see it then. I've only recently gotten over my depression, after my doctor re-prescribed me a liver med. (Yes, a liver med. Everything in our bodies really are connected!)
So anecdotally, mental health doesn't seem to be as reliable as I once thought. I'm not convinced that it's limited to gamers though, except possibly as pertains to social maladjustment. There sure seems to be a lot of that amonst gamers, and I include myself here.