Doesn't matter that the pax had already boarded, even if the plane was already taxiing or even departed it could have been turned back and pax deplaned per the force majeure and unforeseeable conditions clause of the COC about the possibility of denying service to anyone at any point for that kind reason. This is not only in UA's contract but also AA's, DL's, WN's. So indeed the 4 passengers had already boarded legally but they were also legally requested to deplane as long as this came with the relevant compensation and as long as it's demonstrated that it was because of an unforeseen circumstance.
Once legally boarded airlines have to remove 'with cause'. The Dr.'s conditions for removal did not fall under any of the conditions under "Refusal of Transport” (Rule 21) which were the only ones available that they could legally break the Dr.'s contract for the seat he possessed. The IDB order was illegal. The VDB was a negotiation but the pax held all of the cards since they were already legally boarded. Since we have not seen any
force majeure declaration as you imply (pictures or it didn't happen) all we saw was
force applied.