There is something very odd about a PPL holder, whose legal privileges are down to 3000m vis, but who cannot actually navigate under those conditions and is supposed to have an instructor present to go over the water. What is that instructor supposed to be showing him? How to track a VOR and, better still, how to switch on the GPS?
When I did that flight we used a GPS. Neither myself nor the instructor was interested in dead reckoning for about 70 miles in haze.
The instructor will likely be an ATPL hour builder and he will most definitely want to log the flight with himself as PIC, regardless of how the "student" logs it. Somebody will sure as hell be adding up the instructor's logbook entries to see if it adds up to 500 (or whatever) but the "student" will be long forgotten.
I could be wrong on this but I think that in the case of a G-reg plane and a JAA instructor the "non-instructing person" is always PU/T - the successful PPL skills test being the only exception (P1/S).
If the plane was N-reg, then the instructor could be an FAA CFI and the "student" would log it as PIC. The logbook entry would be the same as in the G-reg case.