The 0-Point assignment rule applies in all of those cases, forcing them to be on a nationality-matching crew at all times, except when explicitly captured using an ability like Ransom (swaps and trades aren’t enough).
Fair enough, though I will say that I disagree and I consider it to be a true rules loophole at this point.
Assignment only applies to ships, not islands. “Assignment refers to both the act of placing or loading cargo onto a ship and to the constant state of being carried by that ship.”
They should have worded it more specifically in the Placing Crew section as something like “A crew with a point cost of 0 can be assigned only to a ship that shares its nationality, and can never be on an island.” (addition in italics)