It doesn't seem like she thought you were bluffing. I think she panicked and was not well-equipped to deal with such a situation.
I agree that an efficient, experienced, skilled T would have talked you off that bridge.
Your T didn't seem to know what to do and reacted - e.g. thinking you were playing games so as to keep you as a client, herself not being skilled in dealing with such situations, liability *if* you were to take action. Many factors come into play.
What it does show though is that she was not a good match for you and not the person likely to be able to help you.