AMC1 FCL.050 Recording of flight time says under point
h) When an aircraft carries two or more pilots as members of the operating crew, one of them shall, before the flight commences, be designated by the operator as the aircraft PIC, according to operational requirements, who may delegate the conduct of the flight to another suitably qualified pilot. All flying carried out as PIC is entered in the logbook as ‘PIC’. A pilot flying as ‘PICUS’ or ‘SPIC’ enters flying time as ‘PIC’ but all such entries are to be certified by the PIC or FI in the ‘Remarks’ column of the logbook.
So even if the operator does not care, he has the duty to designate who is PIC and who isn't. PF and PNF does not enter into it, nor on which seat the PIC sits.
To be able to log PICUS time it has to be done under a program which has a method of supervision that has been accepted by the authority, in the UK that was traditionally extremely lax and a signature by the PIC was all that was required, other authorities require an OMD specified and approved training program. During such a program i was flying from the left, taking all decisions, signing the documents but still was not the PIC, i could just log PICUS for that.