Of course many people with depression don't just die of being depressed. That's not what this article is describing.
Depression isn't severe trauma. Severe trauma can cause depression, and what's explained here, is that it can cause death by psychosomatic cause.
Well, what one consciously expresses is not always a match for their inner state.
Second, it's another thing to say "oh god, take me now" than to consider yourself as nearing death. One is a kind of negative wish, while the other is how you view yourself objectively to be going to.
Besides, biological processes are not physical laws. They are statistical phenomena, and people can differ. It's what happens in the aggregate and for most that's examined. In that sense, a counter-example is not enough to take down the phenomenon.
In any case, glad it worked out for you.