Can a director announce the firing of an employee to co-workers at a meeting without first notifying the employee?

You never know what people say so until you hear this from the supervisor, I would not take heed. You may wish to discretely talk to your supervisor if you are concerned or others who were in attendance at the meeting to confirm or deny that statement. If someone else approaches you about the same issue, then I would say it would be fruitful to put your question in writing with the matters that gave rise to your inquiry in the first place. The act itself if actually done is not prudent and is a violation of privacy rights if not other labor laws in your state.