Some complete nonsense here - Noggin is the only one with the correct answer. All in-flight flying supervision carried out by a FI is considered to be 'flight instruction'!
A 'rental checkout' is flying supervision carried out by an instructor who logs it, quite rightly, as P1C. The hirer is an unknown person being cleared for a solo flight - so should log the flight as P1 under supervision with the instructor's name as Commander - BUT the instructor shall also sign the 'remarks' column for the hirer to claim it as P1 under supervision - otherwise it is dual flying.
I am getting a bit suspicious of the motives of some FIEs in assessing the 'experience' achieved in 3 years as I suspect some are keen for applicants to take the expensive FI revalidation skill test in which they have a considerable financial interest.
[ 01 November 2001: Message edited by: BEagle ]