At the end of the day what you log is very much down to the individuals concerned. The CAA is concerned that the stated minima are achieved for licence/rating issue or revalidation.
The Law, Art 28, requires that you log particulars of each flight required "for licence issue or revalidation," to include: the capacity in which you acted.
If two pilots fly together with both acting as pilots i.e. with one checking the other, regardless of whether they hold an examiner authority or a FI rating, provided both are rated to fly the aeroplane, and exercise pilot skill and judgement throughout the flight, P1 and P1U/S describe accurately the situation required in Art 28. Insurance companies may set conditions but they are not in a position to dictate any logging requirements not required in law.
The guidance issued by the CAA is just that, Guidance; it is aimed at ensuring that hours logged towards licence/rating issue and revalidation are acceptable, and therefore meet a minimum safety standard.