I disagree with this. At best, this is a square-rectangle situation. I'd agree that many, maybe even most, stoner metal bands are also doom metal bands, but the vast majority of doom metal bands are not stoner metal. No savvy person would refer to Thou as stoner metal.

And counterintuitive as it sounds, what a band calls themselves actually does not matter at all. Genres are descriptive, not prescriptive; if Depeche Mode came out today and called themselves a black metal band it wouldn't make their music not synthpop/dark wave.