I think you are right PW.
You have been asked to act as a "safety pilot" by an inexperienced PPL who presumably is otherwise qualified to carry out the flight and will limit himself to the authority given by his licence. I think it sounds eminently sensible that he wants someone with far greater experience to accompany him on the trip. That is indeed the function of a safety pilot.
Obviously as a safety pilot you would not act in command other in an emergency ( in which case you can happily log P1 I would suggest ). If you intend to act as P1 in any other event then that would require you to be approved to do so by the relevant authority.
In this case he is obviously the "commander" and you are the experienced observer / passenger/ security blanket ? If he wants you to assume the role of commander he needs to be put straight. I don't blame you being concerned about his lack of experience, but it does seem very straightforward on the face of it.
1) He logs the P1 ( he is signing out the aircraft )
2) His "bum is on the line" as he is P1.
3) Your guidance and help is being sought due your own experience. ( seems very sensible)
4) Lesson 1 "command"