Get the agent's name and let them politely know you'll be sending a note that they do not understand their own rules.
I had this happen at DFW last week. I was on international transit all on AA metal. I'm a OneWorld Sapphire and she wouldn't let me in and was steadfast in her belief that I was trying to slip one past her! Like you I showed her the AA website and she still refused to believe it.
At that point I think all politeness bets are off. Its bad enough not to know the rules, but to ignore them in excusable.