UA (and all carriers) report the reasons for delay to DOT. Making a false statement is a felony. If you truly believe that someone at UA is going to commit a felony to save a $35 hotel voucher, you should absolutely file a complaint with DOT.

But, you are almost certainly barking up the wrong tree. There could well have been perfect WX at ORD, your destination and enroute. Yet, the inbound crew was delayed by WX. Presumably the AA flight was not.

If there was a later flight operating and it had space, I'm not sure that it matters that your scheduled flight was delayed. SDC is there and I take it that the "refusal" to rebook was the lack of space.

As to GA's hanging around gates with no active ongoing process, I'm not sure that's necessary anymore, especially at ORD with CS counters, monitors and the like. The GA is functionally reading off the same screen as you are when you walk over to the departures board.