I thought maybe the change in tow capacity rating was due to the change of 6 to 8 speed during the 2013 MY.
With good set up / weight distribution as proven on tripple scales such as truck stop Cat scales the 1500 can easily tow 7,600 without going over GVWR/payload.
It takes some trial & error and often help from those who are good at hitch adjustment & weight distribution as proven on the scales to get to a more safe stable or more optimum set up. We recently helped this guy;
Baseline him & empty truck.
Steer 3,120
Drive 2,680
Total. 5,800
Axle weight with TT & WDH as set up by RV dealership.
Steer 3,000
Drive 3,980
TT. 6,400
Same Ecodiesel TT & WDH after adjustments.
Steer 3,340
Drive 3,540
TT. 6,520
CVW 14,000
14,000 less 5,800 means his wet TT weighed 8,200.
Afterword a much more safe & stable set up that met all mfg specs. 14,000 met his CVWR of 14,500. 3,340 & 3,540 met his 3,900 axle limits. 1,080 seen TW meets 1,150 receiver rating without WDH allowance. 6,880 made his 6,950 GVWR/payload.
On top of that 1,080 is 15.7% of his 6880 so there is room if he needs to free up more payload such as to fit more people and meet GVWR, without going over any other limits. As he can go down as low as 10 percent TW.
But as Cardhu said wind resistance is or can be the biggest factor. Despite the 8 speed 3.21s don't help. Cardhu also makes a great point about trailer length. A hitch with built in sway control helps a lot but depending on wind every tow can be it's own. In the sticky what have you towed with your 1500 thread I have a pic of me towing a 39' or 35' floorplan TT. But really with a 1500 & family I suggest a floorplan of less than 30'.