OK. So let's assume that CASA's guidance on filling out logbooks is authoritative of who's PIC. That's a (dangerously) invalid assumption, but let's ignore that for now. The guidance at the link Bog Down posted says:
Logging flight time
If you do not receive training during the flight review, log the flight time as 'pilot-in-command under supervision' as per Part 61.095(3) of CASR.
If the flight review requires you to complete flight training, record the flight time as dual flight time.
The quoted text assumes - correctly - that a flight review does not necessarily involve any training.
Question: How does a private pilot who was not required to 'complete flight training' during the 'review' 'log' the review flight time?
Postulation: Merely being 'directed' as to what the reviewing person - FE, PE, ATO or whatever - wants the pilot to do, and what the reviewing person says s/he wants to see along the way, is not "training". Discuss.
PS: Just saw yours, mustafagander. Does the reviewee log ICUS or Dual? What does the guidance linked by Bog Down mean?