United might have been able to avoid all of this by making its passengers aware of the law.
Federal regulations require airlines to pay cash ― lots of it ― to people they bump from flights against their wishes. (They can also cut a check, which is nearly as good.) If bumping a passenger from a domestic flight delays that passenger by more than two hours, the airline has to pay the passenger 400 percent of the fare to the passenger’s destination or first stopover, up to a maximum of $1,350. (The infographic at the end of this post explains the few exceptions to this rule.) Here’s the relevant section of the Code of Federal Regulations:
LII
Multiple investigations, however, have found that airlines
rarely pay passengers the full amount to which they’re entitled. In many cases, this is because the airlines ask for and get volunteers who are willing to accept less money, or even airline miles, for their inconvenience. Airlines are also
supposed to tell passengers at risk of being bumped from overbooked flights how much money they will get if they’re involuntarily bumped, but it’s not clear how often they do that.
In this case, United offered passengers $800, but didn’t get enough volunteers. One reason might be that some of the passengers on the flight in question ― a Sunday evening nonstop from Chicago to Louisville, Kentucky ― were probably entitled to more than that. A one-way ticket from Chicago to Louisville on United next Sunday would run you about $221 ― meaning that, if bumped and delayed more than two hours, you’d be entitled to $884.
Some passengers likely paid even more to be on the flight, and would be entitled to more compensation. And surely the cost to United of offering passengers more money ― even the full $1,350 ― would have been far less than
the negative PR from this episode. The logical thing to do would’ve been to offer more.
I knew it was too good to be true 
I'll certainly defer to you on this issue because this occurred in your jurisdiction. 
But in all seriousness, a professional says this: United should have increased the compensation offered to passengers to entice volunteers, CFRA Research analyst Jim Corridore wrote in a client note Monday. “We think this situation was handled in a deplorable fashion, but note that United has the right to refuse boarding to any passenger for any reason,” he said, adding that “demand for UAL flights are unlikely to be affected by this poor customer service incident.” 
I'm not concerned about whether it was "oversold" or "booked fully" or half full. All the sites I've read say it was within their legal rights to do what they did. Haven't seen anything to the contrary outside some internet lawyers trying to interpret UA policy.
