I could rub a set of 33 x 12.5's x 15's with stock width axles, "standard" back-spacing rims, pretty saggy stock rear springs with an extra leaf and a custom front set up, 1" body lift and new poly body bushing.
Little minor (read invisable) trimming and a little hammer work made contact less likely.
The stiffer your springs or lower your bump-stops, the less rubbing (I didn't run bump stops).
So yes, big, fat tires will probably rub, or atleast you could get them to rub.