This is the video that helped me feel comfortable with 31 inch tires without Johnson Rods. I know your looking for an objective definitive answer on 32's (without Johnson Rods), which I was too, but could not find one.
I did have to remove the hitch to raise the tire up. I did not have to deflate tire to mount it in the spare tire area. Needed a little guidance to initially maneuver around heat shields, but once it was past the edge of the heat shield the tire raised straight up. The last couple of cranks seemed to take a little more effort since the fit is snug.