I'm not certain, but might this cheap fare on Airfares.com be a wholesale or consolidator fare?
From AA's Guarantee:
Exceptions:
The Lowest Fare Guarantee does not apply to unpublished fares that are not available to the general public and fares that cannot be purchased on AA.com. Fares not available to the general public include, but are not limited to, wholesaler fares or consolidator fares.
A $660 fare less than 72 hours before departure makes me suspect that this other website already owns the seat and is trying to unload it - a classic definition of "consolidator."