I imagine AA was following the recommendation from Mexico. I found this on the internet regarding what the requirements are:
Passport validity: The maximum period of time that a visitor may stay in Mexico without a formal visa is six months. Therefore we recommend that your passport, regardless of country of origin, should be valid for a minimum period of six months, however long you intend to stay to avoid any potential problems at the port of entry. Immigration authorities at the port of entry may allow or deny entry of any person into Mexico. If you have a passport that is valid for less than six months and you intend to stay in Mexico for a short period of time—perhaps a vacation—the Immigration Officer might allow you entry, especially if you can show a return air ticket. Notwithstanding this, we recommend that you and your family members hold passports valid for at least six months from the date you plan to enter Mexico.
It's not a Mexican requirement, but is recommended.