The explanation is a bit more complex than you think, and is exactly why the 'alliances' are well, nice marketing. Need to have a bit of a background in the GDS business to understand why.
The GDSes (Sabre, Amadeus, Worldspan, and Galileo) act as middlemen for bookings. Grossly oversimplified, if you're a customer or an airline you can check/upload availability of flights and classes and book them.
Each airline, however, has their own internal reservations system that handles things like boarding passes, checkin, baggage tracking, and (sometimes) seating. People often confuse the two, since Sabre and Amadeus do that as a smaller part of their business along with EDS.
Here's where the problem arises.
For internal stuff, AA uses Sabre (left over from the days when AA owned Sabre). BA signed a HUGE contract with Amadeus to develop their own, cheaper system. LA I think uses Sabre. Can't recall what QF and CX uses. Guess what. The internal systems don't talk to each other.
So...basically, cross your fingers and hope that the BA-Amadeus internal system project works out. If it does, pretty much every airline will be adopting it as Sabre really isn't spending a lot of time dealing with new internal rez development. Then...you might have everything talk to each other and get a true oneworld (and for that matter, other alliances) system. Until then...at least you have an explanation. Cheers.