In case you are interested, please consult the links, the accusations you utter will dissolve into smoke, Bernadotte had clear orders to be at Apolda and not with Davout, there is no proof nor evidence that Davout asked for help - all those suggested ADC proved to be hoaxes, Marbot wasn't even there.
I really invite you to read all those sources mentioned and you will see and what kind a lies and propaganda Bernadotte is confronted and accused.
I understand this to the extent there Boney fawners a extremely jealous of the achievement of Bernadotte, he gained all what Boney was dreaming about.