Death in the Graveyard!

No, "American" was here intended to mean a United States resident. And the actual appearance of the moon on that historical date was not part of the equation. It's a pleasure to see how you guys are all thinking, coming up with ideas and conjectures, some going far beyond the degree of thought commonly shown by those who make up puzzles like this. I ran across this one years ago in some old book, and I don't know what its original source may have been. But here's the solution as it was given:

If you picture the relative positions of the Earth, Moon and Sun, you will see that in order to appear as a thin crescent, the Moon has to be almost directly between the Earth and Sun. That means that the Sun and Moon will appear close together in the sky. So that could happen just after nightfall or just before sunrise, with the Moon just above the horizon and the Sun just below it. But this could not occur at midnight, because then the Sun is a long way below the horizon, and that's where the moon must also be if it appears near the Sun. (It might then appear as a thin crescent to those on the other side of the Earth, but to you it would not be visible at all.)

But there is an exception: If you live near the North or South Pole, there are times of the year when you have continuous or almost-continuous daylight for long periods; so even when the time is midnight by the clock, the Sun could still be just below the horizon. Consequently, in those regions, you COULD see a thin crescent moon at midnight.

So, if the story were true, the man's home would have to be in Alaska. But in 1952, Alaska was only a U.S. territory and not yet a state, so residents of Alaska at that time could not vote in Federal elections.

So the answer is no, he did NOT vote for Eisenhower!