One important factor is being left out. How tall is the tire? The taller the tire, the narrower the rim you can run. For example, if you were trying to make a 31x12.50 (do they even make that?) fit on a 7" rim, you'd have one hell of a sidewall angle and even worse would be trying to get and keep that tire on the rim.
On the other hand, if you were wanting to run a 37x12.50 MTR or the like, I'd say youd be fine, due to all the extra sidewall you have to work with. It wouldnt be as severe of an angle from shoulder to bead. I'd say you'd be okay with a 35x12.50, but a 33x12.50 would be a little iffy. Doable maybe, but pushing it.