Before you get too riled up, know that this stunt does not seem to be very widespread. The comments following each of the below videos lack any sort of information on how to accomplish the feat, and most responses left by the people behind these clips are too busy justifying infinite ammo as anything other than cheating to explain how they made things work. "Since I modified the amount of ammo I have in my clip, it's a mod," wrote impressively self-assured YouTube user 0neThatsExiled in lieu of any word on how the game was "modified."
Happily, since existing examples do not explain how to duplicate this tweak, it's unlikely that you'll encounter the issue within Destiny before the quality assurance team at Bungie has time to obliterate this unintended gameplay issue. Hopefully these self-described modders are enjoying their brief moment of online infamy.