They were obviously incorrect
Also in the same section of AA's CoC, it states
Originally Posted by aa
If we find evidence that you or your agent are using a prohibited practice, we reserve the right to:
Cancel any unused part of the ticket
You were the one in breach of AA's conditions of carriage and AA was fully entitled to take the action
All the time that you lost was down to your being in breach of terms that make up AA's CoC.