First, Bernadotte wasn't stupid. And if it was merely 'an error in judgment' instead of deliberate, I don't see much of a difference. Bernadotte certainly didn't bust him hump to get to Jena and the smoke from the battle was undoubtedly observed from his position and the smoke and perhaps the noise from Auerstadt was certainly there, as Sahuc offered to countermarch to Davout's assistance and was silenced by Bernadotte. That itself is an indicator that the whole episode was deliberate.

Good soldiers and good generals hasten to get into action and assist their comrades. Negligent or treasonous ones do not.

Merely offering excuses for Bernadotte really doesn't cut it. The motivations for his lack of action on 14 October go much deeper than that as far as I can see.

Sincerely,
K