I have a 2011 Nitro and it is'nt listed in the tow guide. If you are to do it, I would go with the dealers suggestion. I can't say for sure why it can't being a standard tranny, but I wouldn't chance it. Not sure running the engine would make any difference to why you can't tow with drive shaft connected.
John, Deb; & our dog, Benji, Forever in our hearts.
2014 Coachmen Leprechaun 319DS V-10
2011 Jeep Liberty Jet & 2014 Jeep Wrangler