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There are a few reasons those idiotic rumors survive, low IQ of the repeaters being a big one. But the main one is that they are a subtext for saying, "There is no f***ing way I am voting for this guy." It doesn't really matter why, because they aren't going to change no matter what proof you shove under their noses.
Of course, those who grab onto false rumors as justification for their vote are hiding their true concern. The biggest one is race.