You're not missing anything. That camper is overweight in every category except the real mfgs rear axle rating, which is 10klb not 6-7klb like shown by the OE specs for srw trucks.
I've hauled my 860 around, same camper basically, around 4500lbs wet/ready to camp.
No problems to date including a HEAVY trip up the Alcan.
You will be over every rim rating unless you go to 19.5s. But I've been running on OE Ram aluminum rims and 3950lb rated toyos.
You'll need supporting suspension mods too. Minimum some extra capacity for the rear springs. Sway bar adviseable too.
Don't freak out, you can haul it safely with your truck but you'll need to spend some $ to make it haul that much well.
All that said, 3500 long bed srw or dually are more appropriate choices. Any srw trucks though will have the same limitations based on tire, wheel ratings.
