I don't suppose either Fain or Meneval actually measured Napoleon so that figure is an estimate.
Getting accurate height measurements is not easy and I would expect that any data on average heights for the period would carry a large margin of error. I don't think there is any value in the 'above average height for the time' argument. People who met him, including Fain, considered him short.
The Chouan Burban-Malabry was 5 pied 1 pouce and was always described as small.