Ahh... that movie again... ahh... the idea behind anonymity... ahh.... how I know I should stay out of this but sometimes can't help myself... ahh....
Anonymity, as far as the traditions and AA is concerned, has little to nothing to do with being ashamed of our past. I don't know a single sober alcoholic who is. Most, in fact, are quite proud of the fact that they're sober. As humble as they try to be about it
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As for the OP, I'd have answered with, "I might know him. Can't say though, as this is an anonymous program", and I'd have said it with a smile. Might have also said, "I don't talk about AA at work. People don't know I'm in the program, and I like to keep it that way". Just an honest, friendly, and direct response.