Visible crew/equipment: In the scene after the storm, the ship moves in the sand. Look at its front and you'll be able to see a wire that moves the ship. It's very visible.
Visible crew/equipment: When they're building the petticoat balloon, the camera slowly goes back. Look at the lower-right corner of the screen: there is a man wearing a stadium jacket. He's a crew member.
Visible crew/equipment: When Vulcan is taking away Baron, look carefully and you'll be able to see a wire in the tail of his coat.
Answer: The Baron is a teller of tall tales and massively exaggerated stories, so it is all from his limited point of view. The Ottomans did have Christian members of staff, especially doctors and such but the treasurer would never be a non-Muslim.