PIC = Pilot In Command, no more and no less.
A PIC cannot suddenly decide that they are not (although I do not believe it is a good idea, I do know that some pilots, when flying together, plan for one to be PIC for the first half of a flight and the other for the second half - I hope no arguments ensue!)
More importantly, in relation to this topic, no matter how bad a pilot they are, no one has the legal authority to take over from the PIC in flight.
A Check Flight is designed to assess the unknown competence (presumably to rent out an aircraft) of a pilot.
I, therefore, disagree with Sam MHN that there is an 'eternal dilemma' on how the Checkee should Log the flight:
-If the Checker is an Instructor the Checkee Logs PUT
-If the Checker is a non-Instructor, Club Check-Out Pilot, the Checkee Logs nothing (as they are simply a Passenger who has been allowed to fly the aircraft).
Flying with an Instructor, the Checkee would, presumably, pay the full cost of the flight.
Flying with a non-Instructor (making full use of cost sharing), the Checkee would, presumably, pay the full cost of the flight LESS One Penny/One Cent - which would need to be paid by the Checker.