To answer this question, it's just that those airlines use the same booking software backend as Qantas, a global system called Amadeus. As a result, you can pull up Qantas PNR's (booking references) on those sites, even if you're not flying on their airline at all. For reasons unknown, Qantas doesn't make as many functions available on their front-end web site as these other airlines do. You're using the other airline's web site as a portal into the same global database, it's just the other sites are able to give more information than Qantas will.
As noted earlier in this thread, LATAM uses a different, competing software suite called Sabre, and part of the challenge is the type of integration between the two, i.e. Qantas bookings on the LATAM codeshares, while saved in Amadeus, are not actually pushed into LATAM's Sabre database until 48h before flight, unlike some other relationships where the integration occurs at time of booking.
