So to bring it back to United, if the station manager says to you ( the captain) tomorrow , " I know your Purser wants to offload passenger Smith because he spat at her when he was taking his seat but in light of the recent event with Dr Dao I am not prepared to authorise bringing security onto the aircraft" .... are you ( the Captain ) legally resoonsible at that point in time to override the station manager ? Or, as has been suggested, does you legal authority not kick in until the aircraft moves under it's own power?
My position is that even if the exact point in time that the Captains authority kicks in is unclear ( as we are finding out) , the Captain does have the legal authority to grant or withhold operational clearance to initiate, terminate or divert the flight, so the Captain does have the authority to not initiate the flight regardless of what we find out about when his or her authority comes alive.
Ie , no skipper worth their salt will go flying if they think it is unsafe reagardless of which section of law says what.