The rules are pretty clear: for aircraft which are certificated for single pilot operation the only time that P1/S can be used is after a successful flight TEST with an EXAMINER. A check-out is not a test and most FIs are not examiners.
Many people seem not to like the rule but in that case they need to start discussions with the CAA about getting it changed.
Logically, if an FI is checking a qualified pilot the FI will be P1 because they are responsible for the conduct of the flight; the person being checked therefore logs Pu/t. Once again, if you don't like this you should take it up with the CAA.
HFD