So does the captain need an ATPL to command a part 23 aeroplane being fliwn multi-crew?
But if it is a SPA operated as multicrew they only need a CPL.
And they also don't need a MCC to be completed
The rules say MJ is correct:
FCL.305 CPL — Privileges and conditions
(a) Privileges. The privileges of the holder of a CPL are, within the appropriate aircraft category, to:
(2) act as PIC or co-pilot of any aircraft engaged in operations other than commercial air transport;
(3) act as PIC in commercial air transport of any single-pilot aircraft subject to the restrictions specified in FCL.060 and in this Subpart;
Not sure this is actually what EASA intended - probably another case of un-joined up rule making with their not realising that some aircraft that only need one pilot do, in fact, require two for certain operations.
Also seems strange to me that multi-crew might be required for a certain flight but that none of the pilots on board need to have been assessed in their MCC skills.
For the OPs original question I think whopity's answer is spot on:
During training the student will be told whether to log PIC or PUT.
Once qualified they may go and fly with a friend who will be PIC but they are now a qualified pilot also sitting behind a set of controls and probably 'taking part' in flying the aircraft. They know they are not PIC and that, obviously, they are not PUT but want to log something and they see in the rules that a PPL holder is allowed to log co-pilot (P2) - but do not know, don't check, or do not care (because they want to 'log hours') that the definition of co-pilot means that the flight must have
required 2 or more pilots.