I don't think there is a salutory effect on officials who "have" to apologize. I think it only makes them angrier and more hostile.
If the employee who triggered this incident has also caused other problems, or does so in the future, she should be fired. If not, forcing her to write an apology she doesn't mean is worth nada.
This is my opinion, with which you are welcome to disagree.
This is the theory that leads to never spanking or disciplining children.