What is the AA equivalent of "bonvoyed" ?
Here's the story that happened to someone I know:
This actually happened: my wife took a flight that landed because of a medical emergency. When she arrived, she missed her connecting flight, so they put her on the next flight and she checked a bag. When she went to check in for her return flight, American Airlines canceled her return ticket, claiming she did not get on the first flight. She argued that she did, but she had thrown out her ticket stub - but they have no record of her taking that flight. Her bag is apparently not a proof. Nine hours of phone calls and ten emails later - she has no proof she was on that flight, they are in denial, and they will not pay her back for her return flight ticket she had to buy.
You see, when American wants to believe something because it suits them (as the terrible bankrupt company they are), they will believe it, even if it doesn't make any sense. And that is Paroh. That's what hardening one's heart means.
Don't be Paroh. And don't fly American ever.