Female fox spirits also like to seduce otherwise upstanding men and lead them astray, just like succubi. So the whole legend is really pretty similar to its Western equivalent, except for that one little Japanese detail about it being a fox instead of a demon. As strange as that is, it does make sense if you consider the difference between Japanese and Christian mythology. Christian mythology includes an entire underworld of evil demonic beings hellbent (literally) on destroying human souls. Shinto mythology is more about the numinous powers inherent in the natural landscape.
When you look at it that way, it makes sense that Westerners would conceive of possession as being the work of malignant spirits, while the Japanese tradition saw the same phenomenon as being connected to the world of nature. In Ireland, possession was thought to be the work of fairies, but that's a topic for another blog.