Clearly a backup boarding pass would have been good, and maybe OP (and others...) will do that from now on. But, as said above, isn't the point of the mobile boarding, in part, to not have to do that? Think trees, environment, cost savings... And whatever you think about that, it's splitting hairs to say that United didn't remove the boarding pass from the app, but instead "stopped displaying it" in the app because "it wasn't valid anymore" because the ticket was "out of sync". If the ticket was still valid (which it seems it was because it was not canceled, he was not offloaded, and was allegedly on original flight and protected on another, then there does not seem to be anything that would indicate that anything has gone wrong with the BP and it seems very reasonable to expect the BP will appear in the app. I'm not aware of anything that would alert someone to the issue of BPs being out of sync.
I recently had a related vanishing BP incident when I provisionally VDB'd on a seemingly oversold flight. Per usual, the GA reserved a seat on a later flight while I waited till boarding finished. In the end my original seat wasn't needed, but that BP had disappeared from my phone. After a brief panic at the scanner, a GA printed my original BP, with my original seat assignment intact. It was an unpleasant eye-opener - I now routinely take a screen shot of my BP if I don't grab a paper one at a kiosk. But I really hate paper passes - they are an inconvenient size, hard to slip in a pocket without mangling. Electronic BPs make airport life much easier...until they don't.