Remember that a tire's advertised width is only its widest width half-way up the sidewall which can be up to several inches wider than its mounting beads. A 33x10.50 tire, for example, will probably have beads that are only 7 or 8" apart which is why you should run a 15x7 or 15x8 wheel for a 10.5" wide tire. Trying to run a 33x10.50 tire on a 15x10 wheel, for example, would result in the tire being forced to position its mounting beads much further apart than they were designed for.
I'd love to hear/read this attacked from another angle, which is how much farther might a 12.5 be able to air down than a 10.5 in the same model of tire, both on a 15x8 wheel. Is it "narrower the wheel, the better" (within reason) or is it more like once it's within the range the tire was designed for, it's enough?