**Sorry for my absence, my wife and I just had a baby boy! **
Yes, you are right there. The controllers are just shift registers, but there is a special sequence (32 zero bits) at the start of data that tells the LED to load the next 16 bits of incoming data, then once it has done that it just shifts all incoming data on to the next LED and it does the same, and so forth down the chain. The LEDs don't have an assigned number as such, it is purely determined by the position in the chain.
If you break the chain then the first LED just becomes LED number 0.
Ben