Edit -
Looking at the PM Support Forum, it appears that whenever you are eligible to rebuy (if you have less than or equal to the threshold amount), then you can rebuy to an amount greater than the threshold amount (if the starting stack and the threshold are both 10,000 and you have 10,000 chips, you can rebuy to a total of 20,000 chips) If you bust out and the threshold is the same or greater than starting stack, AND if the allowable number of rebuys is >1, then the Double Rebuy button appears. If you want to prevent the Double Rebuy button from showing up, then limit the # of rebuys to 1 OR reduce the threshold below the starting stack.
From Version 3.06 onward:
Double rebuy option added to rebuy tournaments. In rebuy tournaments, you can rebuy when your chips are at or below the starting chip level. Previously when a player lost all of their chips, they were presented with "Leave" and "Rebuy" buttons. Since that brought them back to their starting level, they could immediately perform another rebuy using the table menu. Now they are presented with "Leave", "Rebuy", and "Double Rebuy" buttons, which eliminates that second step if they choose.