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The actual policy is published on the AA website. At
https://www.aa.com/i18n/travel-info/arrival-times.jsp , it states
"In most locations, you must be checked in At least 45 minutes before scheduled departure, for flights within the United States"
This seems to be something that could reasonably be relied upon
Checking a bag in , is part of checking in.
Since the bag was not checked in at least 45 minutes before departure , then it was after the listed check in time