I own private property. It's true that I'm free to paint my house an obnoxious color and let it fall into ruin. It doesn't mean that I don't have a responsibility to my neighbors and community to provide upkeep to my house and ensure it's aesthetically pleasing.
Similarly, I believe social media and the media has a larger responsibility to our civic discourse even if they are a private company. Is that a legal obligation? No, but it's a moral obligation.