This isn't really AA focused, the promotional blurb mentions *A too.

I have to laugh though, if you do call AA as they suggest and demand to know if this fare existed, I think you will get a puzzled reaction. There are tons of better ways to demonstrate that fare existed. And asking to be transferred to the rate desk... I'd hope they would hang up on such a request so the rate desk can focus on real work!
There are a range of these services, my sense is they are somewhat fast followers/ indicators of fare sales that you will learn about here first. There were two really deep fare sales this fall (there was another one in October in the $1k range for west coast to EU) and my sense was the premium deals thread alerted us earlier than these services did.