Unfortunately, for many USA residents, AA IS oneworld and can be used interchangeably.
Most of these 'early' morning PAX travelling AA would indeed likely be AAdvantage elite travelling domestic and indeed do not have access.
They would see many more AAdvantage elites trying to use the lounge than non AA *O elites; so the letter would liekly be correct most of the time.
They seem to have thrown the baby out (in the form of non AA *O elites) with the bathwater ...