The only time you can be P1S is for a skills test or LPC - not for check outs, or any other post-PPL flight with an instructor. It's seems quite common for PPLs to log P1S for check rides, which is incorrect.
I dont' disagree with you wb9999 (in fact that's my understanding too).
However I do wonder why we have a flight logging category specifically for a test though - what's the point?
P1S would seem eminently sensible for someone to log if they are being supervised by an instructor. Quite why the rules (apparently) say otherwise defeats me.