What he said is mostly true. However, the v6's and v8's deal with this issue in different ways.
A standard v6 has 3.55 gears and a class 2 hitch. it has a low towing capacity. With the towing package they add a trans cooler, and gear up to 3.73 to gain torque and increase towing capacity.
The v8 however makes no such changes. It has all the power and cooling capacity it needs with or without the towing package. A 2x4 with a class 2 has the same towing capacity, if not maybe a 100 lbs more or so, than a fully loaded 4x4 with the towing package that upgrades to the class 3 hitch. They all have 3.55 gears, which is fine due to the trans having a very low first gear and almost 300 hp and plenty of torque.
You are limited only by your hitch, which you don't want to remove/replace as it is welded to the frame and is an integral part of the structure of the frame. You can however bolt on a class 3 hitch which will give you a max towing capacity of 5k lbs. It bolts to the frame and will drop just below your factory hitch.
There is a thread on here somewhere all about this ^^ I tried to hunt it down for you but could not find it. Search for it if you want more details.
Currently your TRUCK has a max towing capacity of around 7k lbs, I believe the 2x4 lightly equipped are up to about 7250 and a fully loaded 4x4 is around 7,000 flat. That number is how much weight can be moved by the vehicle total, meaning max loaded trailer weight + max vehicle load(how much crap is in the car, including people). So, if you max your 3500lb towing capacity for the hitch, you have about 3500lbs again to add to the vehicle itself.
If you had a class 3 and maxed that hitch you would have only 2500lbs to load into the vehicle. Which is still quite a lot.
The vehicle itself has its own max, the GVWR. The GCWR is the maximum for everything involved.
My last x weighed in at 4200lbs, the new one is probably heavier. lets say 4500lbs
4500(truck)+7000(towing capacity)=GCWR
GCWR=11,500
11,500(GCWR)-3500(max towed with class 2)=8,000
8,000(remaining GCWR)-4500(truck)=3500
The 3500 and the end there is how much you are under your GCWR
Now
GVWR-4500(truck)=how much you can add to your trucks suspended weight. Anything inside or on top of, PLUS the tongue weight of the trailer!
So actually GVWR-4500-300.
Whatever that value is then has to be within the 3500lbs that you have remaining in your GCWR. I doubt though that the GVWR has that much headroom for additional weight.
