I agree that the sister doesn't know Tidy and therefore can't badmouth her to all. Even if she didn't "have" to let GZ see the e-mail, any idiot knows that e-mails can be forwarded. Not knowing Tidy, the sister can't predict what she will do: after all, Tidy has plenty of legitimate grounds for grievance, and after all, GZ has gone absolutely nuts, so the people around GlueSis aren't as predictable as she might have hoped.
In addition, this saga has held MN spellbound, and there's absolutely no way of excluding the possibility that GS is reading this. If she is, I feel a bit sorry for her, absolutely bursting to say something to somebody.
You've been amazingly discreet so far, GlueSis - keep your nerve, or your sister will really make you regret it! 