The numbers on the hitch will only tell you what the hitch itself is rated for, regardless of what it installed on. What is important to note on the hitch is that there are 2 ratings, one w/o a WDH, and for use with a WDH. The manual is correct for your truck, mine is an EXT otherwise same specs as yours, 4WD, 3:42 gears, and 4.2. My tow rating is 4900# due to the extra weight of being an EXT. I'm not sure what site you are getting the larger number from, but that high tow rating is for a SWB, V8 with the lower gear set (4:11 perhaps?).
Keep in mind that the tow rating is only part of what you need to know. That rating assumes only a driver and nothing else in the truck. Add the weight of your family, dog, any gear, etc that you carry in the truck and subtract that from the tow rating. So if your tow rating is 5100# and you carry 500# of gear and people in the TB, your actual tow rating is now 4600#.
Another important number is GCVWR which should be on the sticker in the door. That's the combined total weight of everything, truck, people, gear, and trailer with all the options. Never, under any circumstances should you ever exceed this number.