No matter if United is in the 'right' based on contract or law, as others have stated they handled this extremely poorly. As the situation presented itself they had the ability to raise the 'offer to give up seat' to $1300.
I would be surprised if they would not get a hit at $1000, $1100, etc.
That said, when this all blows over, my fear is the airlines solution for the
good of the customer is to SELL a 'bump free' seat for an extra $50
PS What is the old expression, 'poor planning on your part (United) does not constitute an...'