Ahh, back to this old chestnut.
As has been put by many others, the sensible thing is that if the FI doesn't actually have to say or do anything it should go down as P1/S.
Unfortunately according to LASOR's and stated by M_J, the only time P1/S can be used is for successful completion of a flight test. Since a check out is not a test for licence or rating issue, then the flight should really go down as P/UT. Crazy I know.........
Personally, I've never heard of the Belgrano actually complaining about P1/S apart from in an article in GASIL (I think) a while ago.
So I know you might want to put it down as P1, but if the letter of the law is followed, then you can't.
Personally when I fly with people who I know are competent, then I always get them to put down as P1 and I don't bother logging it. (Couldn't care less about 20 mins or so now!!)
However, if the instructor insists that the flight goes down as dual, then there is no real moaning that will make any difference since in theory they are in the right!