“Should one of them ever seek the office of POTUS, that one would simply need to renounce his or her Caymanian citizenship.”
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Actually, I’m not sure that’s true. While most countries permit their citizens to renounce their citizenship (and I trust that the Caymanians do), “[s]ome countries” (at least according to Wikipedia, http://en.wikipedia.org/wiki/Renunciation_of_citizenship) “may not allow or do not recognize renunciation of citizenship or establish administrative procedures that are essentially impossible to complete.”
Since we would not want a foreign government’s laws to have the power to block an otherwise eligible Presidential candidate, I doubt that actual renunciation of foreign citizenship is required.
I agree with you, if someone HAD to renounce citizenship in an additional country in order to have presidential eligibility here, that would mean that country’s laws have some influence on our laws, which they do not.
Ours operate independently of others.
But though not required, the holder of dual citizenship can certainly choose to renounce the one he does not actually want.