GVRW is the max weight you can carry in the trailer safely (based on axel strength, tires, ect). That means, while you might never carry 13,840 lbs, you can't exceed it safely (you can also get a nice ticket for being overweight). You don't know what the trailer will actually weigh until you load it up and put it on a scale. With that in mind OBD could get away with the 2500HD long bed, but he would have to make sure that he is keeping the trailer not only under GVWR, but under the trucks Max. Trailer Weight and gross combined weight rating (GCWR). If he doesn't he'll have major problems both safety wise and legally.

With all that in mind, you always want to keep a safety margin between what the vehicle can tow (max trailer weight) and what the GCWR of the trailer is. I like to keep over 1,000lb safety margin in normal vehicles. Therefore, if the truck is designed to tow 10,000lbs I wouldn't want to exceed 9,000lbs trailer weight if I don't absolutely have to. In most circumstances it's easier and safer to tow a light load with a heavier duty truck, then it is to tow a heavier load with a lighter truck.

By the way, back in the 70's my grandfather tried moving a 71,000lb trailer with a single axel tractor trailer rated for 65,000lbs. Just moving it 200ft down the road he ended up blowing out two tires. 6,000lbs over isn't really that much when compared with what the truck was designed to pull, but it was enough to exceed the trucks limits. It's always better to be on the safe side.