I know AA refuses to remove miles nowadays, claiming that you did get benefits from the status you have with them and thus you have to credit the miles to them. However I've used my BA card to get into the QF lounge in LAX for years now, without crediting to BA in most occurrences. I've had BA remove credit several times now and they have never mentioned anything about FF benefits depending on crediting miles to their program.

PS: I've even had BA remove my BA number to put my AS number in at the F wing in London and they have not told me that I had to go to the J lounge if I was flying in J. They let me go through to the F lounge.