Here's one that NO ONE can win, I bet.
She says I'm always correcting her. "Well, don't always be wrong then" didn't help even though it was in jest. So I said "how would you know if I'm ALWAYS correcting you, because if you said something that was inaccurate and I didn't say anything about that, then you wouldn't know that I didn't correct you? You would never know how many times I didn't correct you thus you can't possibly say that."
So I stopped and let her go on saying things that are often incorrect and thought OK, I'll make a list of things that I let go and when I get several items I'll say "see, I don't always correct you" until I realized she'll say - "you just did" when I provide examples.
Now I just let her disseminate incorrect info to others as long at it won't be harmful and wait for it to come back and bite. If it doesn't, I figure no harm done and I avoided another black mark. If it does come back to bite and she says anything I won't be able to say " Well I knew you were wrong but you don't want me to correct you" because that will just be a different black mark.
Sometimes you just can't win, and it's smarter to not try - ever.