When I had natural Betta splendens they didn't flare at the mirror. I tried it to see with both my wild male and his offspring.
They also coexisted well, although that was a temporary peace until the idea of spawning hit them. I suspect a lot of the long finned domestic bettas developed not as ornamentals but as ornamental fighters, and a lot of line breeding was aimed at making them more aggressive. The gambling scene is very much alive not only in southeast Asia, but here as a cruel, underground vice. I was in a North American store once when plakats were being unpacked, and while I don't speak Cantonese, the men there weren't excited about the colours of the fish they'd received.
Using a mirror to awaken those instincts and get the Betta to show his fins is an old trick, and some believe it's good exercise. Maybe it is, as the overgrown, unnatural fins of a fancy betta can hold fungus and bacteria in their folds, and maybe an airing out (watering out?) helps. Mostly it's for us to see the fins though.
It's ironic that the number one pretty pet fish in the hobby owes its linebred fancy fins to it being fought to the death by gamblers who wanted a good show.