This is really a silly argument.
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Tell that to the founders and framers.
A few examples...
John Jay, 1787:
Permit me to hint, whether it would not be wise & seasonable to provide a strong check to the admission of Foreigners into the administration of our national Government; and to declare expresly that the Command in chief of the american army shall not be given to, nor devolve on, any but a natural born Citizen.
John Adams, 1776:
On the other hand it could never be our Duty to unite with Britain in too great a humiliation with of France. That our real if not our nominal Independence would consist in our Neutrality. If We united with either Nation, in any future War, We must become too subordinate and dependent on that nation, and should be involved in all European Wars as We had been hitherto. That foreign Powers would find means to corrupt our People to influence our Councils, and in fine We should be little better than Puppetts danced on the Wires of the Cabinetts of Europe. We should be the Sport of European Intrigues and Politicks.
Clearly, they didn't consider it "silly."
It's just looking at your posts today, you seem awfully concerned that the American-born French Dauphin is going to somehow sweep in and "usurp" the Presidency. I wouldn't lose any sleep over it. And who's to say the Dauphin isn't a stalwart conservative? I don't know the guy personally but I'd be hard-pressed to imagine he'd be any worse than Mitt Romney.