Door sticker shows taxable GVWR, when your actual is added axles capacity 5200+6200=11400 lb.
But with TC most of the load goes on rear axle, while not much you can do to use front axle capacity (I put generator on front to do that).
So for your scenario you need to weight your empty rear axle and deduct it from 6200lb capacity. That will give you realistic camper weight you can carry.
Still confirm tires are up to the task.
When it comes to salesman BS and owners ignorance - there is no limit.
Also realistically- the camper listed at 2800 lb will be closer to 3000, or above 4000 loaded for travel.