And why would they close the airplane doors and then make everybody wait 45 minutes, as a matter of policy?

I think the attendant just didn't want to check you in for whatever reason (knew your luggage wouldn't make it, thought you might not make it, was feeling grumpy), and told you a sort of fib. IMHO you should have been allowed to board, especially since you checked in online, presumably in plenty of time.

Thank you for informing me of my error. I was under the impression after flying about 5-10 different flights a month for years that doors closed no sooner than 15min before departure. I never noticed that the doors are closed 45min before departure, even though every one of my boarding passes says scheduled boarding time starts 30min before departure. my bad.

I also see that AA's own conditions of carriage are in error too.

http://www.aa.com/aa/i18nForward.do?...ge.jsp#CheckIn

DOMESTIC TRAVEL
In addition to checking in 30 minutes before departure, you must be present at the departure gate and ready to board at least 15 minutes prior to scheduled departure time to retain your reservation and a seat.