Same here. Badmouthing your private employer in public (and FB is public) has always been grounds for dismissal. There seems to be a question about the union in here, but it seems like a small thing compared to the disparaging comments.
No, the question about the union here is a big
thing. That's the only reason that the NLRB got involved, and it's the only reason that federal labor laws are implicated in what otherwise would be a simple matter of employee misconduct. If the employee's remarks can be construed as having some relationship to union organizing activities at her workplace, then they might very well be protected, and if she was fired for making those remarks in the context of union organizing, then that would constitute an unfair labor practice.