So my understanding is in line with what's been put above, however this is an opportunity to ask a question that someone put to me and I couldn't immediately counter...
Part-FCL says in AMC1 FCL.050 "Recording of flight time":
the applicant for or the holder of a pilot licence may log as PIC time all solo flight time, flight time as SPIC and flight time under supervision provided that such SPIC time and flight time under supervision are countersigned by the instructor;
SPIC is defined as:
"Student pilot-in-command" (SPIC) means a student pilot acting as pilot-in-command on a flight with an instructor where the latter will only observe the student pilot and shall not influence or control the flight of the aircraft
It also says in the AMC:
the holder of an instructor certificate may log as PIC all flight time during which he or she acts as an instructor in an aircraft;
The suggestion was therefore that on a 'checkout' flight, as long as the instructor does not have to provide any guidance or intervene, both parties can log it as PIC time, which seemed wrong to me, but I couldn't counter it in regulation directly - anybody know better?