It sounds like AA reissued the ticket properly (INVOL'D) over to UA, which is all they have to do once confirming space is available.
Unfortunately, UA's system doesn't always (read: rarely) attach the INVOL'D ticket to the newly created reservation.
This means that the agent has to go hunting for it and hook it to the PNR. It's not hard, but you have to know to look for it. Gate Agents SHOULD be aware of it, but sadly, not all agents are good agents.
BP's are easily able to be printed without a Ticket attached...but a passenger absolutely CANNOT be boarded without either a paper or an e-ticket. So for those saying it can be done after the fact...it really can't. Passenger totals can't be updated and a flight can't be closed out without those unticketed passengers being reconciled.
AA sounds like it did everything right, UA everything wrong. Once AA reissues the ticket, it's all UA's problem, even if they can't find the ticket. (Heck, there's even a DOT rule governing them not being able to find an eTicket, as far as I know.)
For those who are worried, just make sure if you're Rule 240'd over to another carrier, you get both the OAL record locater AND the new eticket number. UA's system isn't alone in struggling with this. A lot of airlines' systems don't work perfectly when a PNR is created from an OAL.