That's correct, but calling a bluff can mean different things. In this case, it could be "No, and we don't think you will actually leave" or 'No, goodbye".

My guess is they chose the latter because they don't like employees that run such hard negotiation tactics, and she was becoming too internally disruptive. Either way, any employee should know they are at risk after playing those cards, if not in the short term, then in the long term.