I may be beating either a United passenger or a dead horse with this (not sure which), but:
(1) Whether the offer maxed out at $800 or $1000* (and whether it was a voucher or cash), the fact that they didn't go to $1350 (the DOT-mandated level) plus the other stuff is a bad start on this. It's quite possible that they would've found pax at $1350 cash who wouldn't bite on an $800 voucher.
(2) Absent a safety issue (earlier I mentioned the possibility of weight issues on a smaller plane; for reference, I was on a DL flight DSM-MSP where pax had to move around to balance the load properly), it generally seems to be understood that once you're "scanned in" you're on the flight. Seeing this definition litigated would be fascinating (in the sense of watching a train plow into a truck stuck on a grade crossing being so). My gut says that there's a good chance a jury would not find in United's favor; where that would end up on appeal would be interesting...I could see the case law going anywhere from "the airline can do whatever it wants until it closes the door" to "once you're scanned in you are boarded unless the airline can show some sort of mistake". And of course, it's notable that this isn't a case of malfunctioning computers but the airline "confiscating" seats after boarding had begun.
(2b) As I mentioned earlier, there's a case for some form of negligence on United's part for letting it get this far. Moreover, per the CoC a lot of the language seems to only apply to lack-of-assigned-seat cases. I may just be new to this but I've never heard of a situation where a passenger was IDBed beyond the gate.
(3) Something worth mulling, and indeed often forgotten in this shuffle, is the fact that this was a United Express flight (as far as I can tell it was a Republic Airlines flight). If not for UA's repeated PR issues, if I were Munoz I'd be very hastily throwing Republic under the bus. Hell, if I were Munoz I'd actually be looking at whether I could sue Republic for the resulting damage to the United brand...ok, you can all stop laughing now.
No, really.
Please.
Ok, ok, United doesn't seem to have much of a brand left. Maybe I should have said "trademark". Or something like that.
*Munoz' email says there was a top offer of $1000 but most other sources say $800. Neither case mentions cash vs voucher.