Not that I doubt you, but she says the line with a noticeable optimism. I had assumed it meant something good... I guess she was just being sarcastic.
Thank you, though. In context, it does make sense. If the Doctor had meant that she could tell everyone that she had seen a production of a Shakespeare play, but she misinterpreted it and understood him to mean that she could tell people that she had actually met the real Shakespeare, then yes, I suppose that would lead to some time in a psychiatric ward.