Just because it's wired up to 12v doesn't mean it's a 12v LED. If this is just a typical looking 3mm LED with 2 leads, then look for a Resistor on one of the wires. If it's around 470ohms or so then that's all you'd need to change as it's around a 3v or so LED. Those are Rainbow LEDs and they change colors on their own, the circuitry that controls them is built into the LED. You could use that in a controller, but you'd be better off just getting a new one.
If it's some mess of LEDs and/or uses some control box to make the colors change (would have 3 or more wires going to the LED) then it would be more work to dig into that.
The PS3 has no 5v power source either, only when it's plugged into the USB port will it have 5v in there. The available voltages in the PS3 controllers to use are either straight from the battery, which varies and is not great for LEDs, or the regulated 2.8v in there that is used for powering the Sticks and such, which is a tad low but works for a 3mm Rainbow LED.
Horrible video, but it shows a 3mm Rainbow LED in a PS3 controller on the PS button.
