Had the same argument after a check-out in a Warrior a couple of months back at a club new to me not a million miles from "Vectis". CFI / Owner absolutely adamant that I book and have signed off P1 / S - Club Checkout. No amount of arguing (and there was some) was going to change her mind.
From my point of view I was P1 and if putting an "S" next to it got the hour in the right column, I was not going to get too upset.
The opinion cast was that whenever an instructor is on board, irrespective of the status of the person in the LH seat they (unless firmly trussed up) were the ultimate authority (with ultimate responibility) if it all went to r@t sh't.
This is one that just never goes away.
