I wouldn't trust the dealership, they go off the best case scenario on a unicorn truck.. with no option but what is needed for that max payload / towing number.
For example: My truck is rated at the same payload towing (same rear).. the real payload on the door is only 1375lbs. I'm sure you are higher than that, but I'd double check. Remember, the payload does not take into account the weight of fuel, driver, passengers, hitch, or anything else in / on the truck that did not roll off the assembly line with it from the factory.