In that game, LeBron James did indeed bump coach Mike Brown. Replays are indisputable. Frustrated and jawing at the referees, he spun around back toward the bench and slightly nudged Brown, simply expressing frustration. You turn around, you're mad, you want to hit something. In that immediate moment, Brown fit the bill. No harm done.
It shouldn't be spun into anything bigger than incidental contact. It's not the pinnacle of James' displeasure with what's going on with the Cavs these days, or a defining moment that means irreparable damage has been done during this recent slide.
Brown is on the hot seat, but he was there long before the poor performance in New York. James has always been unhappy that Brown's style doesn't allow Cleveland to run more, yet that same style has produced consecutive 50-win seasons and a Finals appearance...