If you take a multimeter to the PCB, you will find that the power points toward the middle are about 3V. The battery leads all of a sudden are nothing with the cord plugged in (why so many mods dont work when using the battery leads).
The cord provides 5V, yes, but the main circuit of the controller never sees it.
If your LED was getting hot, that is probably becuase it needs less than 3V.