Nonsense. Art 52 merely says:
The commander of an aircraft shall take all reasonable steps to satisfy himself before
the aircraft takes off:...
There's nothing to prevent two people from both reasonably satisfying themselves that those checks have been made, nor is there a requirement to identify the commander in 'booking out'. And of course very often, the actions themselves are delegated. No single action required by law uniquely identifies the commander.
The nonsense is yours,it says commander not commanders.
Or perhaps you interpret 'himself' as two people!?