When I put my 3400 lb. camper in the bed of my truck less than 100 lbs. of that weight is carried by the front wheels. The axle and wheel bearings on your truck should be rated for 8900 lbs. and minus the weight of the truck on the rear wheels will provide the true payload limitation. Newer trucks will have rear axles rated for 10,900 lbs. and this is where the difference lies with respect to maximum payload. The GM 2011 and newer and Ram 2013 and newer trucks also have considerably stronger frames which also helps with the weight and high COG of a camper (and with DRW there is more force applied to the frame than with SRW).
A truck's calculated GVWR is based on the load the front wheels can support plus the rated weight that the rear wheels can support. All the truck manufacturers base their calculation on the weakest link as the truck is configured when it leaves the factory. The weakest link with SRW will be the rims and tires. With DRW it becomes the axle and wheel bearings.
Few trucks will not sag at the rear when a very heavy camper is placed in the bed. This can be fixed by adding extra leaf springs or by using air bags. Some frames are more prone to flexing and an anti-sway bar can help to a degree.
Add 1000 lbs. to allow for food, water, and gear to the "dry weight" of the camper to have a safe ballpark working weight. Lots of campers that have a dry weight of less than 3,000 lbs. and that means a working load of 4,000 lbs. which your truck's axle, wheel bearings, and wheels can handle without problems.