I was looking for something else in the Private Flying forum and found this observation
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Going back to logging flight time....I have always applied a simple rule: If I am legally allowed to fly the plane as P1 then I log as P1.
If it's a club or rental checkout I am legally allowed to fly the plane, so I log P1. If it's a cross-channel checkout (for which there is no legal requirement in the ANO or the rules of the air or anywhere else) I log P1. If it's training for (e.g.) a complex endorsement or a night rating I am not allowed to fly the plane without it, so I log PuT and need an instructor in the plane who logs P1.
I have always applied this rule and never had a problem, although clearly others have, and I think rustle is right that it is more a matter of FIs trying to get more time in their logbooks than a consistent application of the rules.
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I quite agree that this makes sense. However there may be issues of insurance. The Insurers may not grant cover to a pilot wanting to rent without them first having had a check flight with an instructor. In case you could not be in command of the check flight.