First and foremost, this entire incident went way over the top when OP spoke out loud in a sufficiently loud tone to be overheard by someone else some distance away at a major international airport. He did not speak to himself, he spoke ou tloud. There was no reason to utter anything out loud unless OP intended to be heard and if he intended to be heard, what he said was grossly inappropriate to the situation. He may take his business elsewhere, but may well find that such conduct in some parts will find him with the suggestion that he take his business yet elsewhere.
Second, for whatever reason there are a significant number of threads started by people who are challenged to present some proof that they are entitled to entry to a priority line of one kind or another. Spending the money to pay people to police line entry has become an unfortunate necessity because there are indeed so many people who either ignore clearly written signage, think that they are special and that the rules do not apply to them, or have heard from their second cousin's uncle that it is OK to break the rules. While it is easy enough for the check-in agent to deflect these scammers, by the time they are caught out, the line is disrupted and the entire point of the priority area is undercut.
Third, there are many carriers, stations and situations where OP's access to a priority service would have been denied without some proof that he was entitled to that access. Certainly he could have had access to the standard check-in area, but without a printout, an electronic version, a status card or something, he is in for a rude awakening in many locations.
Fourth, while none of us were present, the fact is that he was simply asked a question a second time. If he lied the first time, he lied the second time. There is nothing odd about what is effectively, "are you certain?"
The ultimate resolution here sounds fairly typical. The senior AF person is trained to calm the situation by dislodging the customer without any harm ocurring and other customers being disturbed. As the entire incident is on video because of its location, it is all there for review.