My experience was exactly the same!
Since my "rating" was to be able to tow 15,800 pounds I "cubed out" the camper with everything a new RV'er might need and drove the 6 miles to the scales with a smile on my face. The GMC 2500HD pulled that load with NO EFFORT! I was even passing folks on the highway!
AFTER I weighed it, I squeeked home 15 MPH UNDER the speed limit and went through the camper with a fine toothed comb. I needed to dump 2500 pounds of tools, food, booze, water, and junk to get a passing weight at the CAT scale.
Lou and Laura with Bella - German Short Hair Pointer
2008 GMC Sierra 2500HD Crewcab SB Allison Duramax
2010 Flagstaff 8526RLWS - Superglide 3300
HAM CALLSIGN - KC3FFW