MIA bag check-in is 45 minutes prior to departure; you were probably beyond that time (in actual, 100% accurate time) by the time you were done with inputting all the data, and the kiosk refused the BP because of your being late. It's probably bad programming, as it should still have given you a boarding pass given that you had zero bags.

AA's minimum bag check in time at other (most) airports is as low as 30 minutes.

The agent, as they unfortunately do so many times with impunity, just made stuff up.