Kurt Gödel: hacking the U.S. constitution

I've been wandering through Wikipedia yesterday, and at one point ended up reading the page on Kurt Gödel. Gödel's achievements in the field of logic are indispensable to modern mathematics, and his incompleteness theorem has very far reaching implications in disciplines other than mathematics¹.

It is safe to say he was your typical deep thinker, and inward facing, not-too-closely in touch with reality type of person. This snippet from the page made me laugh real hard, because it so perfectly illustrates certain aspects of a math nerd. Listen:

Einstein and Morgenstern coached Gödel for his U.S. citizenship exam, concerned that their friend's unpredictable behavior might jeopardize his chances. When the Nazi regime was briefly mentioned, Gödel informed the presiding judge that he had discovered a way in which a dictatorship could be legally installed in the United States, through a logical contradiction in the U.S. Constitution. Neither judge, nor Einstein or Morgenstern allowed Gödel to finish his line of thought and he was awarded citizenship.

(emphasis mine)

Does anyone know whether he was allowed to finish his line of thought at some other time? (Not that I'd be personally interested in executing the idea, mind you.)

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¹ Including the fact that free will of any mind is just an illusion it has because it can't contain a complete model of itself it could use for correctly predicting its own behaviour in advance. Enjoyable presentations of incompleteness theorem for layman include Douglas Hofstadter's "Gödel, Escher, Bach" (if you're 16 or older), or Raymond Smullyan's "The Lady or the Tiger?" (if you're under 16).