Rule 25. It's generically called "Denied Boarding", but also deals with the reasons you cannot fly. Just because you have a ticket is no promise that you will actually be on the plane when it takes off.
No, he was boarded already. The rule you're looking for is Rule 21, refusal of transport. It lists specific reasons why you can be removed from the plane, overbooking not being one of them.
He was not being "disorderly, offensive, abusive, or violent" before this incident. I see nothing in Rule 21 that allows United to deboard this passenger.
United screwed this one up (well, I'm not sure if it was United or Republic), and they will do whatever it takes to avoid this from going to a jury. His lawyer will present 20 options on how United could have got the crew to SDF legally, but chose not to "because of corporate greed" (read: a charter jet would've been too expensive).
Their overbooking policies absolutely suck, I've been part of the live auction a few times when they offer 200USD in travel credit usable within 12 months, then 400USD, etc. 800 is the max they go up to, then they will IDB. They put the DB'd pax at ORD to a Ramada that's 50 minutes from ORD in the middle of absolutely nowhere. I wouldn't want to spend 24 hours there, only to get a 800USD "travel credit" on an airline I try to avoid as much as possible anyway.
Had they offered cash, I'm sure there would've been takers, but United decided losing almost 1 billion in market cap and very likely tens of millions in marketing costs they will have to incur to buy back reputation lost because of this incident was better than offering $1000 in cash to 4 people on a plane. Or paying $10k to charter a jet to SDF.
Sheer lunacy from United, I hope the CEO burns because of this, although knowing how long that previous scumbag, Smisek, was there, I doubt that will happen.
United. Putting the "hospital" in "hospitality".