AA does not usually show their A and D seats on their availability displays on certain routes.
The reservation would have to "drill down" to see the availability.
ie. type 106AUGJFKLHR-A in order to see A class displayed, or 106AUGJFKLHR-D in order to see D class displayed.
or they could book the flight in "A" class by typing 0AA100A7AUGJFKLHRNN1, OR "D" class by typing 0AA100D7AUGJFKLHRNN1 etc.
So whenever a booking class is not displayed on itn.net, don't assume it is not available on that flight. The only way to find out would be to call AA or have access to a reservations terminal.