OK, so I went the OLCI route, even though I had done this successfully yesterday. It does show our current seats, and that we are checked in.

However, it makes no sense to this consumer why a website whose function was (in part) to show me a real-time representation of my reservations wouldn't actually talk to the system that holds the reservations. What am I missing here? Does it talk to the AM system when making a reservation? At any other time? If not, how does it ever know when a seat or a flight is available?