I think that it is even simpler than that. The commander is simply the responsible person, the person who gets into trouble if it all goes wrong.
It is simply a responsibility issue. Nothing to do with who chenges switch selections or moves the controls or talks on the radio.
People should refer to a recent accident report where one of those involved claimed to not be the pilot in command but the AAIB found that they were the pilot in command becuase of what they did on the flight.
I think that any instructor on a check flight who claimed not to be pilot in command could easily find the AAIB making the same points.
Regards,
DFC