I've run 285 BFGs on American Racing Baja rims with 4.5" backspacing and had mild rub on the frame with a Revtek 3" suspension lift. I now have 305 BFGs on Mickey Thompson rims with 3 5/8" backspacing and have no rub at all. The backspacing is the key. There are those that run 315s on this site with only 3" lift, but most state there is some amount of rubbing. I personally think that anything over a 33" (285/305) is too big with on 3" lift. 315s (35" tire) look too big. There is a balance of truck height and tire size to keep the truck looking good.
Hope this helps
Hope this helps