Howdy,
I would call AA and tell them about a mistake on my account as I certainly do call when a mistake is made in their favor. The one time I did this (mistake in my favor) they also told me to enjoy the miles and that they would make a note of it for their IT department. To each his own; but I sleep better this way.
In regards to credit for mileage not flown; sometimes it is given - I have asked for it in the past when flying on a full Y ticket and due to missed connections did not make the flight and ended up driving. Officially I think the policy is to deny this - only miles for miles actually flown. However, the one time I did ask for credit; they gave it to me. The way I see it (and perhaps whomever I spoke with at the time saw it) I paid for the flight; part of that ticket price paid for my miles. By not sitting in my seat; at a minimum they used a bit less fuel perhaps - either way - they were out nothing by crediting me with the miles.
This was an exception I believe - not the rule, so it isn't something I would expect. I was happy to get the credit.
Keep the faith,
Pakse