Lots of variables to contribute to what will fit/not fit, which is why you can get so many different answers.
As mentioned, the 10.5's *with stock wheels* (key point) will likely fit and not rub at ANY point with stock suspension, on-road or off. That's been the normal experience with the 10.5's, and mine as well.
You can almost guarantee 12.5's to rub even on-road, tight turns going over bumps, etc. Much more likely than the 10.5's for sure.
If you check with local tire stores, see if any will mount them up for you with a "return" guarantee, that if they rub, you can return them. I was able to do that with my local Discount Tire. BFG AT or MT is all that I could find in the 33x10.5 size that was suitable for mostly on-pavement driving.
