At the end of the day if a club wants you to have a checkout for crossing the briney then it is up to them. However we moan and winge about it the final say on who rents a clubs aircraft is the club and if they have rules you have to follow them or find a new club.
I do however think the enforced club checkout is the biggest con on earth, totally reprehensible and should be banned. If a pilot lacks confidence to do what has to be the simplest thing around then they should ask for support not have it foisted on them.
As for the Instructor logging it as P1, that is also disgusting and people like FFF can come up with as many excuses as the want on why they should be P1 but it still stinks.
I went to LFAT on my own a week after getting my licence. It's not rocket science.