The cyborgs were clearly in the wrong. However, you may have innocently triggered their friend or foe programming by 1) Answering her question about were you were going. It's none of the cyborg's business; and 2) Having a boarding pass in hand instead of a membership card and photo ID. A boarding pass screams: I'm a non-member trying to get in on status and international travel!
Not that there's anything wrong with that, but if you're a member, show your membership card, don't answer questions, and don't take no for an answer.
Huh? Using the BP is easier for both them and you. They don't need id. I never used my card until I started flying AS and want to use the DCA club. Now that I'm not flying UA too often I actually use the card. Irony?