Friend has been pulling a 13.5K 5th wheel for years with a 2005 3/4 ton Duramax. My 2011 handles a 3700 lb. camper with no problems though I added Supersprings and put on Nitto tires rated at 3750 each. The payload capacity is calculated for the truck at the factory based on how the truck is configured at that time. The variable I find time after time that affects the factory payload rating is the wheels and the tires on the different trucks.
With a 1-ton all that changes is the extra set of leaf springs at the rear. There is also the option of DRW to increase payload and towing capacity. Not sure why the manufacturers make the 3/4 and the 1-ton models when all that changes is the leaf springs (except for the 2013 Ram trucks where the 1-ton have a stronger frame than the Ram 2500 trucks).
The GCWR is the key figure. It relates to the stregnth of ALL the components of the truck including the engine bearings, transmission, torque converter, rear differential, frame strength, axle and wheel bearings.
I drove to Las Vegas and back to the Monterey area this past week and decided to count how many SRW trucks and how many DRW trucsk were being used to tow a 5th wheel RV. Counted 40 SRW trucks and 9 DRW trucks towing 5th wheel trailers. Guess no one told the 40 truck and trailer owners that their trucks were not up to the job.