The wifes 1500 crew cab 4x4 Z71 with the 5"10" bed owners manual also said it wasn't recommended for a GN/5th wheel trailer. All of my trucks have to be able to pull a GN trailer.
So I made many 1-800 calls to chevy trying to find out why chevy would make the recommendation. After 3 days of 1-800 run arounds I was finally able to talk with a chevy chassis engineering person.
He says the trucks is just as capable as any other 1500 GM truck but the company didn't want to take the liability of towing a GN or 5th wheel trailer because they felt there wasn't enough clearance around the bed/tail gate and cab with the 5" 10" bed.
I put a bed plate in the wifes truck and now pull my GN trailers with no issues.
If a 5th wheel trailer is pulled pay close attention to cab and tail gate clearances with the short bed crew cab 1500 truck.