I don't understand this person. By all means I would have gotten to the gate early, identified that I was given an offer online and accepted and double checked the offer was still good. Typically, those offers mean nothing as it's not known until end of boarding how many no shows and thus number of seats that have opened up. On occasion when flight is so oversold AA will arrange for volunteers ahead of time and confirm you onto a different flight AHEAD OF TIME. At that point you're reticketed and you would need to recheck in online for your new flight or see an agent/kiosk. That doesn't sound like what happened.