PR and Marketing firms might be especially sensitive about anything that reflects badly on them. On the other hand he didn’t use his real name on his Facebook page, so how many people were aware it was him?
Apparently, at least one too many.
Too many people are idiots with social media. In this case, I would guess one of his FaceBook "friends" was a lefty who decided to screw him.
Stay off facebook. Or at least, post with the viewpoint that anything you post WILL be seen by a humorless HR person at your job.
He used his own picture. He posted the picture of a co-worker’s child without her permission or knowledge. Not cool. Then to insult the child was wrong. He took the picture at work. I think that gives the company the right to fire him.
A person in PR or Marketing should know that you have to assume that ANYTHING you post online will be read by the entire world, and that they will find out who you work for.