AA has seats that are reserved for elites (which I think are called "preferred" seats), and exit seats, and seats that they sell for an additional charge (which may also be called "preferred" seats these days).

But on the Conditions of Carriage page here, AA says:

American does not guarantee to provide any particular seat on the aircraft.

However, rereading the POS policy, it does say that the other seat must be available "without downgrading or unseating another customer". So, for this situation, AA's policy doesn't allow moving people around to accommodate the POS (and my original reply was incorrect on this). For other situations, AA does reserve the right to reshuffle people, the obvious example being an equipment change, and the less obvious and more annoying example a change from say 757 to 767 back to 757, but you lose your favorite seat in the process.

What triggered my reply was mvoight's statement that "the FA has given the POS a free second seat, which is contrary to AA policy." A free second seat is not contrary to AA policy, if one can be found without "downgrading or unseating another customer". It is the "unseating another customer" that is contrary to AA policy, whether to a better or worse seat. A "free second seat" is only contrary to AA policy if there is no seat left on the aircraft, i.e. needing to VDB or IDB or (perhaps?) refusing a standby to make the seat available.