So why the misconception? The misconception results from the difference between the French pouce and British inch of the time period. The pouce was equal to 2.71 cm and the inch was equal to 2.54 cm. This conversion confusion is the result of the missing five inches in Napoleon's height.
It's amazing that a simple confusion resulting from conversion differences has led to such a large misconception that has carried through for nearly two centuries! That's how many misconceptions start. A tiny mistake is made that carries through to a larger mistake that gets repeated over and over until it becomes common 'knowledge'. Misconceptions take place in all fields of study and it's the job of any good scholar to work to debunk those misconceptions.