I came across this, from Bourrienne's Memoirs of Napoleon. However, I could not find "Histoire du Consulat et de l'Empire, tome 7" to which it refers.
http://www.gutenberg.org/ebooks/3567 (vol 3, ch 6)

The complaints of Bernadotte's conduct on the 14th of October
1806. when he gave no assistance to Davoust in repulsing the main
body of the Prussians at Aneratadt, are well known. Jomini says
that Davoust proposed to Bernadotte to march with him, and even
offered him the command of the two corps. Bernadotte refused, and
marched away to Dornburg, where he was of no use, "his obstinacy,
difficult to explain, nearly compromised both Davoust and the
success of the battle;" See also Thiers (tome vii. p. 172), who
attributes Bernadotte's conduct to a profound aversion for Davoust
conceived on the most frivolous grounds.

Is there anything to support this?