IANAE, but note that actual pilots have already commented.
I’m not sure why non experts are so confident that the CVR operates in line with the engines running, if that’s the case why didn’t the pilots discuss their ‘illegal’ flight plans prior to starting the engines? seems a bit dumb not to?
Is it not more likely that if the CVR is operating automatically it runs when the aircraft is energised, so if it is running from an APU it would continue to operate which is most likely the case here, as the circuit breaker wasn’t pulled to stop it. Engines running or not is possibly an irrelevance.
Again, IANAE. but the conspiracy theory stuff here is lame.