What single incident proves the king and duke to be nearly as stupid as the townspeople?

The King and Duke get into an argument about the money and start accusing each other of stealing the cash and hiding it, especially since they had added the proceeds of the Royal Nonesuch to the pot. The Duke finally physically attacks the King and forces him say that he took the money. Next, both men get drunk, but Huck notices the King never again admits to taking the money and rather denies it at every opportunity.