That to me is a 'could happen to anyone' moment. Careless on the part of United, shouldn't have happened, but it did, and to my mind once the mistake had been realised the airline did the right thing. As to not notifying her, illustration if ever it were needed that you should check the departure board at the airport, especially if you checked in on line hours earlier. Announcements? In my recent recollection, foreign airlines in Australia and the US make announcements in English and their own language (Cathay in Cantonese not Mandarin - screw you Beijing) but local ones do so only in English.
Most likely untrue, but funny, I recall a story of an Air New Zealand flight to Los Angeles being announced as having 'continued service to Auckland'. One passenger allegedly heard this as 'to Oakland' and stayed on board. Then, two hours into the flight ....