RIvera has always been clumsy with his words, and unable to consider the consequences of what he is saying prior to saying it. What head coach blurts out 'We can be eliminated today?' after a game with playoff implications. Even if you DON'T know the answer to that question, which trust me, is bad enough... to actually say it out loud and letting everyone know that you just lost a game and had no idea it might end your season - it's just insane for someone at that level of responsibility not to have the situational awareness not to say it.
Just like getting asked about the new OC you brought in. It was a leading question, but most media questions ARE leading questions. You have to actually be smart enough and savvy enough to a) know that you don't have to answer every question posed, and b) to know what kind of answers are going to stir controversy. He wasn't able to do either of those and this is just the latest instance.