He's either got amazingly fast fingers, or he's using a macro controller. See, something that alot of people don't realize is that, in a doubleshot, two shots isn't the limit. A doubleshot happens when you pull the trigger twice in the time it takes for the first burst to fire. If you can pull the trigger three, four, five times in the time that it takes that first burst to fire, you'll shoot as many shots.
My guess is that he's just using a macro controller, a controller that you can program to hit a button, or combination of buttons continuously. He programmed the controller to hit the right trigger, hit the macro button, then hit X. He COULD just have fast fingers, but I find that really hard to believe, since he seems to miss his timing alot when he's hitting the X button.
Edit - I didn't see at first that he was still triple/quadshotting with no reserve ammo. Only way that I can think of for him to do that is if he was hardmodding.