If the instructor rating is required for the flight, then you've got an instructor who is P1. Otherwise you haven't.
That sounds fair.
Presuming that a fully licensed pilot is flying an aircraft within the privileges of their license, as issued by the authority, an
instructor is not required to accompany them. If a
pilot, authorized by the aircraft owner's insurer, is requested to go for a check flight - but it's not "instruction" because the customer pilot
is duly licensed, that [second] pilot would not be logging the flying time, as they are not
instructing as required by the license issuing authority.