I think we have made this far too complicated.
Perhaps, but it's reached a thought exercise status in my mind.
If Insurance or Group/Club rules specify a checkout with an experienced pilot then it can be decided before flight who will be PIC however, for all the reasons listed in other posts, I think PIC should be the Checker with the Checkee being a passenger and recording nothing in their logbook.
So I read from that that a properly licensed PPL will exercise the privileges of their license while flying a plane, and paying for the privilege, probably satisfy the expectations of the checker, and record no piloting time in their log book? That sounds wrong to me! Checker pilot records PIC time for a flight when they probably did not touch the controls at all, and there is no written record of the person who did fly the plane? That does not sound to me like accurate "logging" at all, it sounds like false record keeping.
If it is agreed or implied that one pilot will intervene, or take over, if he deems it necessary, at any time during the flight, then that pilot is PIC.
Is this defined in regulation some where? I don't agree at all. Many times I have flown as a passenger, who once airborne, by prior agreement, will take over flying the plane for a specific purpose (like assessing a change to the aircraft, or demonstrating a newly installed feature, or equipment) I hardly think of myself as PIC for the flight, and do not log that time.
For the newer or less certain pilots reading this thread, though not necessarily participating, I would encourage you to understand and if needed, discuss the aircraft provider's policies in this respect, as an element of your business arrangement with them....