But when you look at the options he is either:
A. PIC
B. ICUS
C. Dual
A is not possible as stated becaues of 5.81, but B. ICUS is "In COMMAND Under Supervision" so he is still in Command and as such with the wording "(1) A private (aeroplane) pilot must not fly an aeroplane as pilot in COMMAND" it therefore precludes this option and of course if its C then he is with an Instructor and you might as well do the flight as a BFR!!
So sure he could fly and not log the time, but lookout if CASA got wind of it (Ie, theres an incident, you got ramped or another pilot doesn't particular like either of you) and felt like making an example. Its only Illegal if you get caught of course!