Technically, yes, you need a union to adhere to the Advisory Circular.
"appropriate third party, such as..."
means, only a union?
I'm not seeing where "appropriate third party", means only one, singular choice. I read it as labor organization being one of different types of third party entities that meet the intent of that section. Otherwise, if a union is the only way to adhere to the AC, then the AC....as written.....is stated in a vague and open-ended manner by the FAA. I would think they'd tighten that up a bit so as to be more specific?
That said, I can understand that a labor union would commonly be the accepted third party entity, merely because of it's position. That would make sense.