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How long is what kept on file? The fact you had a producer, or copies of your documents?
I don't think it is of any consequence even if they did retain everything on file. All a producer does it to confirm that you are legally covered to drive the car you were in at that time. It isn't a criminal record, it doesn't have to be declared to your insurer and apart from the hassle of having to go to the police station I can't see any downside from it at all.