So I've been reading a couple of different opinions lately that have made some interesting points.
I think we've established that the flight was not actually overbooked/oversold. There was a seat for every passenger that checked in, the problem arose when they had to move these 4 crew members to Louisville.
This is important, because one of the allegations is that, based on that information, United violated their own Contract of Carriage. Specifically, rules 21 and 25.
One of the semantic issues is that apparently the term "boarding" is not defined in their CoC. So what is the definition of boarding? I would argue that once you're past the door of the aircraft, you're "boarded".
Having made that argument, UAL's options in the CoC decrease significantly. Because they're no longer denying someone boarding (which, even if they were, they can deny boarding for an oversold flight, but there appears to be no provision in their CoC for denying boarding for moving employees around).
So now we look at their rule for Refusal of Transport (rule 21). Basically, the list of reasons they can boot you off the plane.
https://www.united.com/web/en-US/content/contract-of-carriage.aspx#sec21 (source)
I think there's only one condition that UAL may try to use, and that's:
C. Force Majeure and Other Unforeseeable Conditions – Whenever such action is necessary or advisable by reason of weather or other conditions beyond UA’s control including, but not limited to, acts of God, force majeure, strikes, civil commotions, embargoes, wars, hostilities, terrorist activities, or disturbances, whether actual, threatened, or reported.
I think that if UAL is going to try to claim that their crew schedule issue fits into Force Majeure, I think they're going to see this s***-storm reignite big time.