Bernadotte was collocated with Davout when he was given a copy of Napoleon's 2200 13 October order by Davout after the latter gave him a written copy after receiving it at 0300 14 October. Bernadotte was undoubtedly aware that Davout had made contact with an advancing Prussian force of undetermined strength on the afternoon of 13 October west of Naumburg. Both corps were located in the vicinity of Naumburg.
Bernadotte did not start south to Dornberg until after he was given a copy of the order by Davout which stated by Berthier that if he was with Davout they could march together.
The situation had changed on the afternoon of the 13th with contact being made with the Prussians. Bernadotte staying to the letter of an order that was now overcome by events clearly indicates that he had no intention of supporting Davout no matter what the situation was. Those are the actions of a thorough pedant or of abandoning a comrade-in-arms before a fight began.
Bernadotte was, in the words of Doc Holiday in the movie 'Tombstone': 'a skunk of the lowest order.'
In short, Bernadotte knowingly abandoned Davout. If he had supported Davout, I doubt very seriously that Napoleon would have been bothered by 'disobeying' an outdated order. Napoleon expected his corps commanders to use their heads and act or react to a changing situations. Davout certainly did; Bernadotte did not.
Sincerely,
K