I imagine you're not in a customer service business. It's obvious the person had a ticket and, through no fault of his own, somebody pulled it (almost certainly a previous gate agent). I assume UA will get paid for the first ticket and now for the (more expensive) second ticket.

I suppose it's a good idea for every pax travelling with a paper ticket to review the remaining documents after each check-in, but do YOU want to hold them liable for the full loss if they don't do this and an agent makes a mistake?

I don't think UA did the right thing here. Do you?