FWIW the AAngels at LAX just showed me the entire screen of how it went down. A ticket was issued on United last night with the fare paid.
Seems to be a UA issue - that being said, AAngels mentioned that even if the fare wasn't paid, AA And UA have an agreement in place to move passengers and then settle up later; they were actually horrified that UA would leave people hanging like that especially at that hour. They also reiterated that the boarding pass is the key, as you only can get one with a valid ticket.
Seems like signs are pointing to UA being the main culprit here.