Your interpretation is incorrect. AJ faked out the catcher - he made the move towards his dugout to GET AROUND the catcher, and when he saw the catcher start walking away he turned and ran...
I agree with you. AJ's behaviour in my eyes was cheating. He faked out the catcher and he faked out the ump. The ump called him safe because he was not sure if his out call had been correct. Since the Angels had taken his out call seriously and started leaving the field, the honest thing to do would have been to call him out end the inning and let them go on to the next inning. What were the Sox afraid of? Everything was tied up. They just showed kids around the country it's okay to cheat if you can get away with it.