When a PPL holder comes to me for a routine checkout (club check) I recognise that they are qualified to take the aeroplane and act as PIC. The routine check however is one of responsibilty. The club is acting responsibly by having such a rule. The pilot is acting responsibly by subjecting themself to the check. As is agreed, the law doesn't demand this. The check is voluntary. Before the flight however, I make it clear beyond doubt that should I consider it necessary to take command I will do so and they must agree to this.
For this reason the pilot should be PIC unless it is decided that they are to have instruction and that being the purpose of the flight. In such a case it isn't then a checkout at all but an instructional flight.
Agreed, exactly what I do.