Imagine any truck like the old playground teeter-totter.
One side goes up, the other goes down.
Same with trucks and their ratings. Say an F150 with a regular cab and 8 foot box is rated at the 11,300 you mentioned.
Now add on an extended cab or crew cab. Rating just went down because of added weight to the vehicle.
Now add on the weight of a fifth wheel hitch to the vehicle. Again, ratings go down.
Even changing the interior options, or going from an XLT version to a Lariat will change ratings, as those options, small as they are, weigh something.
So be aware of how different configurations for any vehicle will indeed change what that vehicle is rated to tow. And fine print reading may result in finding out that the vehicle you want is not rated to tow what you need.
And, as others have said, an F150 is really on the lower limit of any 32 foot fifth wheel. For in fifth wheel towing, it is NOT can your vehicle pull the trailer. You should be asking can this vehicle CARRY the hitch weight of a loaded fifth wheel. And again, the F150 is really at the very lowest end of pickups when it comes to the ability to carry a load.