I'm wondering if that is the problem - they haven't properly implemented the paid seating logic for codeshare flights, so they just block all seat assignments for those. As far as I can tell I'm in a booking class that should get free seating, but it could definitely be that my understanding is wrong and it isn't the booking class, but the fare that determines that (i.e. their fare that gets you free seats might book into any of the booking classes, while the lowest fare can do that as well, so it isn't based on booking class but on the underlying fare, which they cannot see for codeshares).

BTW: I'm not really happy to book the non-codeshare as the FI fares are way higher than the AS fares for the same flights, and also earn only a fraction of the AS miles.