Both sides are expressing what I regard to be defensible views of communism. You and Ashton are addressing the political philosophy, Alex and others are talking about the actual expression of what is claimed, by name by the participants, to be a communist party. You're both right. But you're using the term to mean two different things and trying to show that the other is wrong.
Discussion doesn't depend upon "correct" usage. It depends on the participants agreeing on what the terms mean - whether a dictionary or encyclopedia agrees or not. Yes, things are simpler if we agree on an unbiased reference.
You're not going to convince Alex that he's wrong, and vice versa, until you come to a consensus about the terms you're using. Just as one has to come to a consensus about the use of the word free in "free software", "free lunch", "free electron", "free energy", etc.
Discussions about terminology aren't very interesting, IMO....
Cheers,
Scott.