From AA's Guarantee:
Exceptions:
The Lowest Fare Guarantee does not apply to . . . fares that cannot be purchased on AA.com.
Huh!!??? They don't have to match a fare if it is not available on aa.com!!?? Now, isn't that a meaningless guarantee: "If you find a fare elsewhere that is lower than you can find on aa.com, we will match it, unless you can't find that lower fare on aa.com."
OK, sounds a lot like Catch 22 to me.