AA not reissuing tickets correctly happened not once, but three separate times to me, so I tend to believe some sort of AA screw up is involved in the story.
Last time it happened to me when I was flying AA the next morning, but the flight was cancelled, and in the evening before the flight AA rebooked me on WestJet flight. I wake up in the morning and before going to the airport I check my reservation and see it was cancelled. Turns out AA did not reissue the tickets and WestJet cancelled the unticketed reservation. It was a major stress to get the tickets reinstated just a couple of hours before the flight.
The OP story seems to be a result of a technical issue of two airlines not properly working together - a very common issue. And then nobody takes responsibility and points fingers at each other.