An argument doesn't assume, but it states. Assumption is something people do. When somebody makes a statement regarding "what an argument assumes", the meaning is that they are speculating beyond what the argument is stating.
So I don't agree with you, but thank you for the discussion.
Thank you for playing the role of the logic police. I guess it can sometimes be unreasonably hard to talk in a simple forum like this in a chill manner without having to deal with people's (IMO) misplaced pedantry. So be it. I'll try to be more scientific the next time.