Ok, now keep in mind that all makes of tires are technically different sizes as the tire sizing is a ratio of tread width to sidewall height and all that jazz.
A kumho Road Venture AT KL78 is the tire I picked off tirerack.com
to make my point.
in stock size 245 75R 16
that tire is 30.5" tall
In stock TRD off-road package size 265 70R 16
that tire is 30.6" tall
up one size to 265 75R 16
that tire is 31.6" tall 4 tenths of an inch shy of the 32's you were looking for.
up two sizes to 285 75R 16
that tire is now 32.8" tall. 2 tenths of an inch shy of a 33" tire.
I stand by my original assertion that you can go up one tire size to a 32" tire with just the billy 5100's and not have any rub.
To go to 285's that is a two tire size jump, and nearly a 33" tire and that will rub.
The point is that the tire's measurements change in all directions every time you change one of the measurements, because it is a ratio. So by changing both the tread and the sidewall size it is a two tire size jump.
All brands of tires will differ slightly so a 285 75R 16 Cooper or BFG will not necessarily be exactly 32.8", but it will be reasonably close.
I hope I have cleared that up.