This is one of the main differences between flying in Oz and the US - it was so much easier (not necessarily better) when you just had to remember "if you are rated/licenced for the aircraft type and the operation and you were the sole manipulator of the controls during the flight, you can log PIC". I remember several flights when I still had a PPL in the US when an instructor would acompany me to fulfil insurance requirements (needed 200+ hours), but I could still log PIC and had to do everything associated with the flight.
Sadly nobody seems to think this a good idea on this side of the Pacific. Hence every time you take a check flight with an instructor in order to fulfil the insurance requirements to hire the aircraft for a joy flight, you will alternately get told to log as ICUS or Dual, depending which day of the week it is.
The bottom line here has to be who the operator (I presume there is an AOC involved somewhere in all of this???) designates as PIC, and I don't think the insurance company is going to swallow that there is one PIC for CAR purposes and another under the requirements of the policy. ICUS a very real possibility?