Whose who?
Well, for a start your boss does not have a private arrangement with the CAA and nor does anyone else.
For me, a club check is simply that. The arrangement has no lawful authority. The flight is simply a contractual matter between the owner and the hirer. The pilot being checked therefore should log the flight as P1 unless the instructor has had to interfere.
Therefore, for me, the question is more to do with what the instructor logs. LASORS states: Section A, Appendix B, Page 40, Recording of Pilot Function: para 1c. The holder of an instructor rating may log as pilot-in-command all flight time during which he acts as an instructor in an aeroplane/helicopter or ..... etc.
The question is: Are you acting as an instructor during a club check? If the pilots licence and experience is valid including the 90 day rule then anyone could do the check for the owner. If the 90 day rule or some other element could not be complied with then only an instructor could accompany. You would therefore be, somewhat obviously, acting as an instructor in the circumstances.
The CAA without doubt encourage any arrangement whereby an instructor always undertakes routine checks. There are precendents where both pilots log PIC. In certain circumstances during CPL/IR training - the student logs SPIC and the instructor PIC. The Captain of multi-crew aircraft when resting continues to log PIC although the co-pilot will also log PIC simultaneously, when they are handling pilot, during the captains rest.