I have to check my sources to see where the position of 1er and 3e corps were at the 12th and at the 13th and what Murat was doing.
So far, it seems to me that the Etat - Major had the impression that 3e corps way to Apolda was via Naumburg (crossing the Saale) and Bernadotte via Dornburg, both had the identical objective.
Davout was in a better starting position there his units were well placed, Bernadotte seemed to have to do a lot of marching - to even get to Dornburg.
Steve gaves us powerful tools with the article of Titeux, the book of Barton, along with Foucart and maps - it is possible to asses the situation of the unit commanders as the days unfold.
The usual opinionated victimization of past and present of Bernadotte won't help, though it is interesting why he was victimized and still is.