Thanks Infinity. It seems you were contemplating exactly what I was: essentially having the tap be a branch circuit and not a feeder. This begs a larger question, that was brought up in your thread, of protecting the equipment. However I dont see any blanket clause in the NEC that generally says utilization equipment must be protected at its rating. Sure we have transformers, panel boards, motors....but if the instructions in my widget stretcher are silent on overcurrent protection?
I find the "ampacity not less than the rating of the device supplied by the tap conductors" to be a strange statement. It makes sense if the "device" is a OCPD because that would protect the tap conductors from overload, but if its not..?
If the device is a motor with integral overload protection, that will limit the current through the branch/tap wires except in the case of a short circuit.
If a short circuit occurs, up in the instantaneous trip range of the 1000A breaker, then that breaker will also protect the 500A wiring just fine.
But what if the device is a widget stretcher which contains a widget heater as well, since hot widgets stretch better, as every body knows?
Now the motor overloads will keep the motor from pulling more than 300A for any significant period of time. And the heater's normal draw is just 200A. So far so good. But a fault inside the heater could cause it to pull 700A instead. Under those conditions the total load will be 1000A. The 1000A breaker will not open, but the 500A tap wires will overheat.
The only reason that you can have the motor branch wires protected by a higher current breaker is that the motor itself contains an overload. If it does not, then you will have to size the conductors by the OCPD amps instead, which will require more copper.
If iwire's lighting board does not have internal OCPD or at least current limiting, then you would have to have a separate OCPD protecting the tap conductors IF it is a branch circuit tap and it is not one of the kinds of loads enumerated in the 210.19(A)(4) exception.
Remember that the branch tap conditions are set in 210.19(A), including the tap exception in (A)(4), as referenced in 240.21(A). That is one of your hypothetical conditions.
Feeder taps, which fit the scenario you originally described, are governed by 240.21(B) and following instead, and pretty much require that there be downstream overcurrent protection of some sort.