Okay, knestle PM'd me saying he doesn't have a DMM, so I went and tested one of these jacks. The lug on the side of the jack is tied to the metal shell of the jack, always. The lug directly aft of that one is tied to the sleeve of the plug and to the shell, but only when there's something plugged into the jack.
So, the difference between these two lugs is that if you run the ground wire to the one on the back end of the jack, it's connected to the shell of the jack only when there's something plugged in. If it weren't insulated from the case, this would cause the case to be grounded only when something is plugged in, which probably isn't helpful for a heapdhone amp. It's simplest, then, to use the lug on the side, since it's connected to the sleeve of the plug when it matters, and to the case always, when not insulated from it.