PAG,
You asked if other trades are denied the facility of demonstrating their skills, to a civvie, using RAF equipment. The answer is no, they are not denied such resources, provided that the civilian examiner poses no security risk, or does not cost the RAF any money. As others have already indicated, the CAA examiner does not pose a threat, he has been cleared on the station and auth'd to fly as pax on a properly scheduled training flight.
There are many cases of civilian examiners awarding grades (or monitoring) Service personnel, of all trades, in their daily jobs. For example, if a chef, about to leave the RAF, wanted to invite a civvie catering instructor/examiner into the JR's restaurant kitchen to prove his skill and get a certifcate then, in principle, he can provided he doesn't get in the way, etc. The fact that it doesn't happen is not the issue.
Hope this helps.
Regards
Kev