All right. My two cents on the incident.
1. This guy has been in this referee group for a while, he is respected... so, I believe him when he says he has never kicked out a sideline before. As for the other stuff, that is a he said she said situation. I can't make a judgment on that.
2. Does the referee have the authority to remove a parent.... or a sideline by extrapolation? The answer is: sort of.
The referee only has jurisdiction over the soccer game, that means everything inside the touchlines and the technical areas. He has no technical power over a parent, who is a free person not subject to the whims of another in America. However, what a referee can do is stop the game (which he has authority over) and refuse to resume officiating the game until he gets what he wants. If it seems no one will comply with his request, then he can walk off the field, thereby ending the game officially. He would then be required to send a report to his association/assignor for his reasons. For the most part, the association will back up the referee as long as states he has a legitimate cause.
I have personally kicked out only a handful of parents myself. I refuse to address the parents, look them in eye or their general direction, or generally acknowledge their existence. When I kicked them out I stopped the game, told the coach I would not resume until a parent was removed. "Which parent" they asked 1 time. I said, "I'm not picky, choose one". (they were just being difficult, they knew which one). But I honestly didn't care. If they chose the wrong one but the sideline shut up, problem solved, if they chose the wrong one and the sideline didn't shut up, I would repeat the process until they kicked out the right one.
In conclusion, when is the last time you have seen an EPL referee point to some drunkard in the stand and go, "I want that one gone"