Fired over social media comments?

I got called by my manager today because someone had taken a screenshot of a comment (that I don't recall have made, and I've asked Facebook for such information). Apparently someone took a screenshot of, went to my profile, which is private and from there to LinkedIn, search my company and email them. My manager told me that most likely HR will call me to discuss. My company has social media policies, but about the company itself. Isn't my out of the office time private? Can I actually and legally get fired for something out of work and irrelevant to work and the company??