We've towed our 16' Uhaul
with a Jeep Liberty for a year now and yes, due to the spare tire mount, the trailer place where we had the hitch put on sold
us the longer ball mount. The couple who owned the trailer before us also had a Liberty (Renegade) but they changed their spare tire design to angle somehow and used a regular hitch.
I honestly never felt real comfortable with the extension, to me it didn't feel like there was enough metal in the reciever for the weight
of the tongue but your 13 is lighter thus less tongue weight
and should be fine.