I don't know why it is, but the question had been posted on other boards and received the same response. I'll be reading Betta books to ascertain that this is true and that there is a reason for it.
If you look at it again, it doesn't seem to be perfectly symmetrical, but I'd expect a more ragged appearance should the betta be "blowing its tail"...I think that it has engaged in trimming it instead.
I have a Betta that constantly keeps his tail short (I wish he wouldn't since he has a gorgeous tail but he doesn't think so) and have NEVER had a problem with any kind of infection. I would say as long as he doesn't trim it extremely short you should be fine with never having to treat him. BTW, my betta has had his tail trimmed on and off (sometimes he likes it long other times he doesn't) since I've had him which has been just over a year. Anyway, hope this helps.