To summarise: time spent with a non-instructor check pilot is not loggable
Sorry, don't gree. If you are simply having a check out, say on a club aircraft, then you can log it as P1. The check out is simply a private as opposed to legal requirement.
On the other hand, differences training
is a legal requirement, must be with an instructor, and is logged as Pu/T. This is so even though the regulations to not specify any minimum standard for the differences training.