(I understand the remarks were job related)
Why should an employer be allowed to fire an employee for off-time remarks? When did working for a company translate into 24/7 speech control?
There's a serious misunderstanding of the First Amendment here.
Free speech does not mean you can say anything you want with no consequences whatsoever. Of course there are consequences for what we say. All free speech means is you cannot be prosecuted or muzzled by the government. Period.
When an employee is out disparaging their employer and/or clients in public, especially in writing on something like facebook, it harms the employer and destroys that person's credibility in their position. If an employee is harmful to the employer, the employer can fire them. Free speech has nothing to do with it. Nobody is prosecuting her for saying it, nobody sailed in and censored her facebook page, but she does has to accept the consequences for her actions.