I absolutely think that personal issues should be handled privately. It is ridiculous to publicly end a friendship or any relationship via social media. These celebrities are the first ones who are complaining when they think people are intruding into their lives, so they need to learn how to deal with things without the public knowing.
Once upon a time there was a thing called tact. Unfortunately, the world of social media seems to have blown this to the wayside. Because we can access information about people (and their relationships) instantly, many feel they owe it to the world to let everyone know about their life, including the private details. And then it becomes a vicious cycle. I don't think it's a bad thing to take a break from all the social media accounts and focus on what matters in your life, like REAL people and REAL relationships.
Yes, a serious relationship should be ended privately and not through social media. In today's society, people are more concerned with seeking the attention of fans and others over social media than they are with the actual events in their lives. This really is a private matter and it should be handled that way.
I really don't know what is happening with this generation, we have resorted to living our lives in the full glare of the public in the name of being digitized. People are washing dirty linen in public without chills. Kat Von D ought to have ended the friendship privately just like they met privately.