Same problem- slightly different fix
I found the gas tank vapor fitting broken on top of the gas tank as you guys have described. The tell tale sign was the gas tank cap light coming on and staying on. The brake cable does pull down on the line as described by thombull above and the plastic fitting will break. I'm not sure if later model JKs have the same issue but I found out one of my friends in the local club with the same 2011 had the same issue and the dealer's answer was to replace the gas tank- $1100. I decided I wanted to try and fix it for a little less so I picked up some 3/8 stainless tubing at Ace and some Seal All (Update the Seal All didnt last. I pulled it out this mornin, went back in with JB Weld) .
I drilled out the broken piece of the fitting and the plastic piece on the tank. I used a small tubing cutter and the 3/16 drill bit and the 3/16 tubing made for a nice fit. I opened up the compressed tubing with a smaller drill to keep the tube open so I don't have any issues filling the tank. The only issue I had was that my relocated Evap cannister was right in the way so I had to remove it to get the drill in there. You can get a regular size drill motor in there without having to drop the tank.
I left the fitting to cure overnight and it felt nice and solid the next morning.
The code cleared and hopefully it wont break again. I'm hoping the stainless will be strong enough to reinforce the fitting. I cut the wire ties holding the line in place to give it some room to flex and I am going to move the brake line under the evap line.
I hope this helps somebody,