It does not sound like she was "bumped" for reasons that would qualify under a denied boarding policy (e.g. oversold or etc), but rather she was late to checkin. And besides, those rules might not apply to China (but others may know specifically). Nevertheless, it would not hurt to write and ask for UA compensation for the delay and subsequent trouble with the connection.
The way I read it is the the first (original, #5) attempt was due to missing the check-in deadline (or that gave them an excuse). The attempt the next day (#11) might be due to a denied boarding. Of course, without a printed itinerary that shows confirmed, how do you prove that, right?