OP says that he is aware of the policy for his rental. Just figured that if he engaged for long enough, someone would give in to get him off the line. This time it didn't.

The argument that Avis ought to cave this time because others have caved under other circumstances just proves that OP has a habit of doing this. Maybe Avis has notes in his account because he's done it before? Who knows, maybe he's had a good run and now it's over.