As with all sources at variance with each other, evaluate each from the perspective of the source's author and what he had to gain by his observation, what his relationship to Napoleon was at the time, and when his source was published. If they are all contradicting each other, then assign blame--or not--as you wish.
I've always thought Naps wanted the duke alive, the better to castigate him in a very public way as a traitor and a useless Bourbon pawn in the pay of England. More bang for his buck that way. Dead he was of no use, and an embarrassment, requiring enormous spin to make it work, somehow.