If you want a reference, point your students towards LASORS, section A, appendix 1. (I think that's right, but my installation of Adobe Acrobat isn't working at the moment so I can't download LASORS to check it.) This contains a list of the various different ways of logging flight time.
It only lists two times you can log P1/S. One, as you say, as a successful flight test for the grant of a license or rating in accordance with JARs. The other is a co-pilot acting as captain under the supervision of the captain. Since you can't have a co-pilot on a single-pilot aircraft, this doesn't apply.
The reason there is so much debate about the types of flight you are asking about is because they are not listed in the table. Assuming that P1/S isn't an option, you have two choices:
1) Your student (the person in the left hand seat) logs PUT, you log P1. You are captain, so you make any command decisions.
2) Your student logs P1, and you are a passenger and can't log the flight. There are plenty of instructors who are happy to do this, but since you are nothing more than a passenger, you can't do any more than advise your student if you don't agree with the command decisions which he is making.
This decision obviously needs to be made before the flight, because who is in charge is not something you want to be discussing in an emergency.
There is an argument which says that your students should log P1/S rather than PUT in the first case. After all, neither is listed in LASORS, so neither is more correct than the other. I don't really have a good counter-argument to that, other than, if it comes down to it (e.g. applying for a license with absolute minimum time, or an insurance claim) I'd rather err on the side of caution. I shouldn't think there are many people who are so desperate for the extra hour or three of P1 time that it's worth taking the risk of logging the time as P1/S when this isn't sanctioned.
FFF
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Edit - have now got Adobe Acrobat working, and checked my reference. Sorry - I got it wrong, it's actually Section A, Appendix B. Page 40 of LASORS, which can be found (confusingly) on page 56 of 610 in
this document