This is interesting and relevant, especially if you are trying to hit the 100hrs mark.
I am of the school of though that it is as I deem it. If the instructor is in the RH seat and gives no input to the flight then s/he is merely there as an observer from the hirer of the Aircraft so I am in effect P1 carrying a safety pilot to satisfy the clubs insurance.
If the instructor "instructs" in any useful manner the it is P/ut.
I throw in the any useful manner bit as some instructors seem to try to imprint their SOPS on the world!
I guess this kind of goes along StrateandLevel school of thought.
I would be interested to know how many people have done shared multi time in the USA and both logged P1. Not expecting any one to own up to that one though