Just to clear up some things..
1. The picture of the controller in the OP is the CG version, while the ones in the videos are the older Matrix one. The LEDs in the CG are Common Cathode and the Trigger lines go high to fire, so every single reference to voltage/ground is bass ackwards with respect to that picture and is probably causing some confusion. In reference to the Matrix controller it's correct though.
2. This is also limited by the game, as if the pulses are too fast the controller/game will only see the line as being held low all the time and not each individual pulse, so it will act like the Trigger was pulled and held, and all you'll get is one shot when pressing the button.
3. Not to take anything from the ingenuity of the mod but, compared to using a simple 555 timer circuit where ya can fine tune the speed ya need, not to mention being able to use any of the 4 player slots without having to move the wire, this isn't a very good idea for people to be doing to their controllers as the results are going to be all over the place.
4. This does not work on the newer Wireless CG version of board or on the newer Wired CL version board. I don't have a Matrix version Wired controller here to test, but I'd guess it also does not work on it either.
If anyone is curious what the REAL problem here is with it not working, it's the battery voltage. I tried it, it didn't work, but clearly it does from the videos, so I went looking for the problem. With a PSU (3v) or AA pack (3.0v) the thing didn't work at all, but it DID work just fine with a PnC pack (2.6v). So while yes this does in fact work, it also does in fact not work. It's just way too sporadic to be considered reliable IMHO. Good job on discovering it and all, but for the people that want a good solid Rapid Fire setup, with the option to fine tune the speed from game to game to get the most from the weapon they're using, then they should look into building themselves a nice 555 timer circuit to do the job. Spend the money on a kit if ya like, it's your money, but making it yourself isn't that difficult and is much more rewarding, plus ya get to learn some about electronics along the way, and yes any of these type of mods can be made to use the Trigger for the button with just a SPDT or DPDT switch and cutting a trace.
EDIT: Also, this isn't something I'd recommend or do to any controller, take it or leave it, just my opinion on the mod.