Virtually every Jewish person in this country (or any country) has a choice under the 1950 Israeli law, Right of Return, to claim Israeli citizenship. Does that mean it's impossible for an American Jew to be a "natural born citizen", giving your definition?
Hear how I rule. Of course not. They are Natural Born American Citizens who are being given the choice to accept the OFFER of citizenship from another country. It is a choice they need not accept, and since their parents were not Israeli ciizens, but American citizens at the time of their birth, they are Natural Born Citizens with an unexercised option that every American has: i.e., to leave. And like every Naural Born American Citizen, it they might even be able to come back and run for office.
The more interesting question is, since they do not have to renounce American Citizenship, would they be eligible to run if they accepted it and didn't leave?
Example 14,998 from the book, "Tough Cases." Get me The Dentist!