My 2000 C2500 had 3800 lbs of payload per door sticker. An additional 1600 or so if I added the axle capacities. I've pulled a 12000 lb equipment trailer via pintle hitch with out too many issues. It had poor low end gearing, so it stalled out on anything over 10-12% in grade.
At the end of the day, there person is correct, if the truck has the payload to handle the trailer, go for it.
Performance wise, depending upon the motor, gears in trans and pumpkins, along with torque for getting going, hp for max speed on a freeway grade.....it may not meet the drivers spec......
Marty