"Kurt Gödel, meet David Addington"
Gödel and the mathematicians' fear of language. repeats, with the original telling of the story.

On September 13, 1971, Oskar Morgenstern recorded the following memory of Kurt Gödel’s 1948 Trenton interview with an official of the Immigration and Naturalization Service (INS).

“[Gödel] rather excitedly told me that in looking at the Constitution, to his distress, he had found some inner contradictions and that he could show how in a perfectly legal manner it would be possible for somebody to become a dictator and set up a Fascist regime never intended by those who drew up the Constitution. I told him that it was most unlikely that such events would ever occur, even assuming that he was right, which of course I doubted. But he was persistent and so we had many talks about this particular point. I tried to persuade him that he should avoid bringing up such matters at the examination before the court in Trenton, and I also told Einstein about it: he was horrified that such an idea had occurred to Gödel, and he also told him he should not worry about these things nor discuss that matter.

Many months went by and finally the date for the examination in Trenton came. On that particular day, I picked up Gödel in my car. He sat in the back and then we went to pick up Einstein at his house on Mercer Street, and from there we drove to Trenton. While we were driving, Einstein turned around a little and said, “Now Gödel, are you really well prepared for this examination?” Of course, this remark upset Gödel tremendously, which was exactly what Einstein intended and he was greatly amused when he saw the worry on Gödel’s face.

After this remark, Gödel wanted to discuss all sorts of questions relating to the Constitution of the United States and his forthcoming examination. Einstein, how- ever, rather deliberately, turned the conversation around. He told Gödel and me at great length that he had just read a rather voluminous account as to how it came that the Russians adopted the Greek Orthodox religion of Catholicism instead of the Roman Catholic faith.... Gödel did not want to hear any of this but Einstein in his sardonic way insisted on going into incredible details of this entire history, while I was trying to drive through the increasingly dense traffic at Trenton.

When we came to Trenton, we were ushered into a big room, and while normal- ly the witnesses are questioned separately from the candidate, because of Einstein’s appearance, an exception was made and all three of us were invited to sit down together, Gödel, in the center. The examiner first asked Einstein and then me whether we thought Gödel would make a good citizen. We assured him that this would certainly be the case, that he was a distinguished man, etc. And then he turned to Gödel and said, Now, Mr. Gödel, where do you come from?
Gödel: Where I come from? Austria.
The examiner: What kind of government did you have in Austria?
Gödel: It was a republic, but the constitution was such that it finally was changed into a dictatorship.
The examiner: Oh! This is very bad. This could not happen in this country.
Gödel: Oh, yes, I can prove it.
So of all the possible questions, just that critical one was asked by the examiner.
Einstein and I were horrified during this exchange; the examiner was intelligent enough to quickly quieten Gödel and broke off the examination at this point, greatly to our relief.”

I googled my reference above to find the first time I used it, and found Balkin and Levinson [pdf], which only makes sense. If you don't get the joke, and want to, start here, and end here [pdf p.44]
And again: it has it's own tag