Reading that and hearing some other people talk anti-union sentiments, the "third-partys get in the way" line is one of the sneakiest ones. That line is designed to make you feel stripped of agency, as if you had more directly negotiating with your boss.
The workers are the union, so they are in the negotiation room, directly negotiating with the boss. You can't fit all the workers in the room, so the workers select a group from their ranks to send to the table.
It burns me up to hear that line because it's so indefensible, yet it's so common.