This actually raises a serious point, which I've raised elsewhere. I'd be very curious to know if the ref has the right to simply tell the people in his earpiece that, no, he's not going over to consult the monitor. They presumably cannot order him to do so. He is the on-pitch match referee.
It would be very controversial, of course. Why would he do such a thing? Well, precisely because of this: he would be well within his rights to say, "I was right up with the game, only a few yards away, I was following it closely, I'm a trained referee at elite level, and I saw no clear and obvious error. You may have seen something playing it several times over in slow motion, but neither I nor the other two helping me out on the pitch saw it. It thus does not come under the heading of what you can legitimately intervene for. So thanks — no monitor. I stand by my decision.”