Does it have the tow package? If so, tow it.
IMO these are the biggest BS ratings that Ford has ever come out with. Think about it; 5.4 last year can tow over 11K, now 5.0 with more HP and TQ can't even break 10K. (I think max with the 5.0 is 8800) It's just a numbers game to get folks into the 3.5EB or 6.2.
If my 2000 5.4 (260HP/350TQ) with 3.55 gears is rated to tow 7300lbs, your 2011 F150 can easily do much more. Just look at the specs of breaks and what have you. Most of them exceed most Superduties.
Also in my 8+ years as a firefighter/medic I've been to hundreds if not thousands of accidents and I've never heard of a vehicle being weighed. I would say that the vast majority of law enforcement officers have no idea what GCVWR is.