Christianity.com sums up the reasons why the myth is wide of the mark: "[Atchison] was entitled to the position only if the President–elect and vice–president–elect died. He had no more taken the presidential oath of office than Zachary Taylor. Furthermore, his term as President pro tempore of the Senate expired with the 30th Congress on March 3, two days before Taylor took the oath."
History.com goes into much more detail – including the fact that not only a plaque on a statue in Plattsburg, Missouri, where Atchison died in 1886, but also the headstone of his grave in the same town, both promulgate the myth that he was "President for one day".
© Haydn Thompson 2020