Yes, GIJoeCam, you are correct.
In the perfect world of engineer test, gov regulations and insurance liability, you should never exceed your weight ratings. On occasion, & to answer wvscrew's queston, 1500 lbs of gravel spread evenly & a short drive will not cause undue harm to the components of a truck. Every day, maybe, but occassionally, I do not believe so.
A 02 screw w/ the 5.4 has a payload cap of about 1800 lbs. Minus apprx 300 lbs for fluids, minus apprx 200 lbs for driver yields apprx 1300 lbs of payload capicity. Distributed evenly will max out the axles at their cap & = the GVWR of 6600 lbs.
A SCREW has a bed volume of 44.2 cu ft. A yard of dirt, soil, gravel, will weigh apprx 2500 lbs. (rough estimate used in the dirt moving industry)
44 cf = apprx 4074 lbs. Do not do that to your truck. I know you have seen it done. As someone who has been around equpment & trucks forever, I promise you, exceeding the cap. by 10-20 % occasionally will not cause failure or a noticeable decrease in usable life. Dumptrucks, backhoes, excavators, farm tractors, work trucks, forklifts, etc... used by many companies would not get as much work done if they did not exceed rated caps. I have spec'ed out alot of equip & most customers view the caps as a suggestion or range, kinda like we use the speed limit. The manufacturers know this & build things to handle it.