This is a touch nut to crack. Were her posts made publicly available, or could only her friends see the posts? If only her "friends" could see the post, and a friended co-worker reported the remarks, that would be like a friend tattling about the water-cooler conversation, and isn't illegal. However, if this woman made comments that anyone on Facebook or the internet could read, that's basically publishing her thoughts, which could count as libel.
I don't agree with current libel or slander laws (I don't think individuals should carry enough clout to actually slander anyone or anything in the first place), but too many people seem to think the internet is just a great place to be a dickhead.
The company handled this poorly. If they had enough complaints to fire her anyway, that should have been their official reason. Why mention the facebook postings and open themselves up to a lawsuit? This would be like firing someone for not showing up to work, then making some comment about their race. You just lost any credibility you had.