In situations like these, I find it is very helpful to refer to the
actual governing contractual or legal terms. Per United's
Contract of Carriage, one can find the contract's Definition of "Oversold Flight" which is:
"Oversold Flight means a flight where there are more Passengers holding valid confirmed Tickets that check-in for the flight within the prescribed check-in time than there are available seats." (emphasis added)
Further, "Passenger" is defined as:
"Passenger means any person, except members of the crew, carried or holding a confirmed reservation to be carried in an aircraft with the consent of the carrier." (emphasis added)
Now, while it is true that the undefined term "crew" most likely means those crew members actively working the flight in question, the fact is that the flight could not be considered an "Oversold Flight" in any case as the extra 4 pax/crew almost certainly had not checked-in "within the prescribed check-in time". UA is wrong to call this an "Oversold Flight" and has no prescribed remedy under its CoC Rule 25 - Denied Boarding Compensation. UA can either try to claim that its need to transport additional crew qualifies as a "Force Majeure Event", otherwise this situation really isn't contemplated within the CoC.