What you're missing is the second main dimension in towing, pin (or tongue) weight.
Sure the truck is rated to tow 14,000lbs worth of 5th wheel trailer, but a 5th wheel travel trailer generally has 25%+ of its overall weight on the pin. In a 14,000lb trailer that is 3500lbs, not counting the weight of the hitch or the weight of the people in the cab or the weight of the fuel.
Ain't no diesel F250 on the market with 3500lbs of payload capacity.
I agree, I see lots of F250 and 2500 series trucks pulling big 5th wheels. Most of 'em are sagging in the rear as they go down the road. That's not good for driver or passenger comfort, let alone stability and handling. Sure it's safe given the odds of being in an accident are slim even if you try, but that's really not the issue at hand, even though people will try to tell you it is.