This is one of the many reasons why you don't book partner awards with Iberia Avios. And it is also why you regularly monitor your IB+ award bookings and obtain the partner PNR in order to monitor your booking in two places. (especially since AA are notorious for schedule changes)

AA is basically correct and your only recourse is probably to sue IB for reimbursement of your replacement flights. As the AA agent said, the ticket wasn't reissued properly after a schedule change / flight number alteration by your travel agent , which is this case is IB.