Could be. Let's have a look at the fine print on those documents he carried.. boarding pass and ticket and such.
Maybe something he clicked "I agree" on for online booking.
You're discussing what you think should be.. not what IS.
In United's Contract of carriage, they discuss the terms for a "Denied Boarding" situation (due to overbooking):
https://www.united.com/web/en-US/content/contract-of-carriage.aspx#sec25
In the "Refusal of Service" section they discuss the conditions under which they can deny service and remove you from the plane. This situation isn't covered.
https://www.united.com/web/en-US/content/contract-of-carriage.aspx#sec21
So, the overbooking situation needs to be handled before they allow passengers onto the plane. Once boarded, they cannot remove a passenger without cause (disorderly conduct, emergency, etc.).