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Don't think a recruiter would automatically associate in the way you suggest
Agree. A former colleague of mine was BA management in the 90s at the time of the naughtiness between BA and the bearded one. He went for a new job and the recruiter asked "Did you have anything to do with the 'dirty tricks' campaign?". What a stupid question! There can only be one answer, regardless of the truth.
It's like a policeman asking you if you have got any drugs, or the US immigration form that says 'tick here if you are a spy' etc.
Anyway, my colleague got the job.