Re: flat tires on a motorized bicycle (do not turn tire inside out)
As a guy who's been on bicycle for primary transportation (by choice, mind you) since the 1980's, 150+K miles pedaled, please hear me out:
Yes, it's totally possible to mess up a tire bead. For tubeless use.
A wire tire bead is always salvageable for tubed use as long as the sidewall is intact, from my experience.
Even if a tire's bead has separated it's possible to use a tire, from my experience. Again, I speak only for mostly intact sidewalls and use with tubes (I have yet to go tubeless on bicycles). A little background: I grew up in an area of California with the dreaded goathead thorns so I'd like to think I know my way around flat tires and have ridden enough miles to have worn all kinds of tires out. I have used tires with folding/kevlar beads and true wire beads. Wire beads can be less forgiving, given the nature of wire, but turning one inside out shouldn't ruin it. Granted, it's my humble opinion that you didn't need to do that to find the offending flat-maker, but we all have our methods regarding location of such. Still, that should not have ruined the tire.
It's a good thing you saved the tire, because I think it's still usable.
Bend it to its natural shape, put it in the sun for a few hours and it should be up to the task when you fill it with a tube and inflate it again.