She may have seen it as helping someone deal with a stressful system rather than it being against you personally. She has not dealt with it well as, rather than asking you if you wanted to discuss it, which she should have realised that you cannot do as it presumably involves confidential personnel matters, she should just have said something like 'I think that I should tell you that I am helping X with her case'. You could then have discussed it with her as a general policy issue.
You won't be able to stay friends with her and you have obviously now made that decision.
You need to be careful how you handle it internally as any comments you make could be misconstrued and used against you. Is it any part of her job to counsel staff? If it is, then to some extent it depends on how close your friendship is but she may have felt that she could separate her professional duty and your friendship. I think that she made the wrong decision but some people compartmentalise things more than others. It is possible that she was being disloyal, even spiteful. It is also possible that she thought this employee needed helping in standing up to the department and that she should do that. She should have referred the employee to her union if she has one but it is possible that there was no other help available.