I would have had no problem pointing the wrong thing out if she hadn't 'got it' herself, but I knew she would.
The thing to avoid here is being the know-it-all who tells everyone how things should be done when, given just a second, those people would figure it out anyway. Nobody likes that guy.
The question is why pointing out something wrong would have automatically damaged your relationship with her ?
Everyone can agree that making mistake is natural. Can't people learn not to get upset when being told they made one ?
One way is by exposure in an environment where the feedback is factual and without drama.