Total bollocks actualy.
You ever thought a immobiliser may have cut in ?
Will a(petrol) car run without power , think we're all agreed on no it won't, where does the power come from ?, the battery, where does the battery get it from ?, what condition does the engine need to be in in order to supply electricity, RUNNING, the system is kept live.
Ask any half brained track racer why the FIA ONLY approve battery cutouts that also cut the ecu feed, and the ignition feed.
Same way a motorbike without a battery, such as a serious dirt or trials bike stays running, ie it has something, usually a magneto producing electricity.
Simple fact of life once the BATTERY excited alternator starts charging, it doesn't stop charging so long as alternator is turning, this is why after switching off, by killing the power to the ecu/ignition it needs to be re excited through the 12v live delivered by the charge warning light for it to start charging again, the ecu ignition system lights etc, have no idea where the power comes from, it comes down the same wires, that the alternator is attached to, if you put on way too much electrical load on the alternator it would cut the engine, purely due to low voltage not being suffecient for spark.
The battery is mainly there for the starter motor, that is why really early cars with starter handles didn't always have batteries, but still ran perfectly, it also serves a function to help stabilise the voltage, and to supply current when the demand exceeds the supply(from the alternator).
tabetha