Don't forget that there is also a theory with alcohol and writing being intertwined, which is a depressant.
As for me, I have clinical depression. Specifically major depressive disorder. When it's not keeping me from writing at all, or indeed having any interest in anything, I will admit I tend to write from that place. So I fit the theory in a way, as I write a lot. I don't however generally share what I write, and I have trouble being prolific. Part of the reason for this is I simply lose the will to write.
So this poses a problem, as I believe people like me who struggle with severe depression would have difficulty ever being recognized as a writer. Perhaps after my death it'll be different. That said, a lot of artists do make art from a dark place. I don't think there are any hard lines. Creativity in some aspects is a way to cope with the horrors and vagaries of life. But not all writers will be depressed, and not all depressed will be writers.