Bettas that bite their own fins... seems... odd to me that they'd do it out of boredom, and that they'd do it out of stress. I have another theory, and to accurately confirm it we need to look at bettas that actually bite.
I've never had a betta tail bite, but I've never had a betta that flared daily, or was in a situation where they would flair daily (divided tanks).
So I think it has something to do with them flaring, perhaps when they flare and jerk all over the place, they see their tail in their peripheral vision, and attack thinking it is another betta, or their target.
I do doubt a betta can slowly reach back and bite their tail, so I imagine it as a rapid and quick movement, such as when hyped up on testosterone or flaring?
All the "tail biting" victims I have seen usualy have before and after pics, and the before pic they are flaring, which means they probably do it on a regular basis, for whatever reason....