Is not the captain in an absurd position, with all the responsibility but none of the knowledge?
It seems to me that the whole idea of the captain (or the ground personnel) deciding who is to fly or not is a relic of bygone days. Airplanes today are like mid sized hotels, with service staff, while the management is locked behind the cockpit doors.
It would be more consistent with civil rights and reality to accept that once people pass security, they are qualified to be on board. If the airplane is oversold, the auction mechanism allows for the market to clear.