We still do not have an answer to the simple question of whether AA cancelled the flight(s) or whether OP cancelled them.
If the former, this is a surprising thread because according to many, AA is doing an efficient and fast jobs of granting and then processing refunds. If the latter, it goes without saying that neither the COC nor DOT rule require a refund and whether a refund is due is a matter for the fare rules of the specific ticket.