Like it or not, with the advent of social media, it has become our business, look at the example of people who have been fired for Tweets, because they do reflect on the employer.
That is a good point. As the environment more and more resembles a fish bowl, the connection between person and business image grows tighter.
Decades ago when there was only Usenet on the interwebs, it was customary for folks to disclaim that their views had anything to do with their office’s views. It was only considerate to do.