The outburst doesn't bother me. I am also really bothered by how the sports media, and media at large, prioritizes drama and conflict over information and I think you're right that Durant is reacting to stories not just about himself but also his buddies.
That said, it never ceases to amaze how much the people who claim to not care what other people think about them, care about what other people think about them. You know who actually didn't care? Tim Duncan. All of these players who say things like, "Whatever, it doesn't bother me..." and then go on a defensive diatribe about the thing that supposedly doesn't bother them need to find some way to gain some self awareness.