No it is not correct. Ownership is irrelevant. What you are probably refering to is the statement contained in the ANO Schedule 7:
(5) Subject to paragraph (6), the holder is entitled to fly as pilot in command of an aeroplane of a type or class specified in an instructor’s rating included in the licence on a flight for the purpose of aerial work which consists of instruction or testing in a club environment.
It used to say in a flying club in which both persons are members. As there is no legal definition of a flying club within the ANO, it is all fairly meanigless. It takes no account of schools which are not clubs and the CAA's own examiners do not operate in a club environment. When JAR-FCL was introduced in 1999, all SLMG training came under the auspices of the BGA not the LAA.