I'd always thought that the ultimate authority granted to the pilot in command of an airplane was to ensure the safe completion of the flight. I know this was a BA plane, but in the US the authority is granted by part 91 of the FARs, so applies to small aircraft too.
MikeGranby, what FAR gives the pilot in command the authority over anything that does not affect the operation of the aircraft? What statute (FAR) would the PIC use to justify the forcing of people to sing Irish Folk Songs? If the order given by the pilot doesn't affect the operation of the flight, I'm guessing it is not a lawful order.
Now the captain wears another hat of authority, that of senior management representative of the airline. If he makes a management decision that the airline doesn't want to transport a passenger, then fair enough. In this case I'd expect the airline to pay compensation, but in this case I'd expect the airline to back the captain's management decision.
Any lawyers?