This is nothing to do with CPL privileges at all. It is absolutely and ENTIRELY to do with the purpose of the flight and following on from that the airworthiness standards that are required of the aircraft that is to be used.
If you do Aerial Work then the a/c must have a C of A and be maintained to PT standards.
The exemptions allow an aircraft that does not conform to the standards required for Aerial Work to be used by making the flight a Private Flight rather than Aerial Work in certain defined circumstances. It's nothing whatsoever to do with the privileges of the PIC and everything to do with the purpose of the flight. If it's a Private Flight the PIC can be a PPL, BCPL, CPL, or ATPL and if he has the requisite rating he can instruct. Whether or not he can be remunerated will be dependent on his licence privileges.