how does Dr Robertson determine that the kind and duke are frauds?

The King gives a speech and foolishly digresses. A Doctor Robinson enters the crowd, hears the King and laughs heartily, calling the King a fraud because his British accent is such a bad imitation. The townspeople rally around the King, who has been so generous, and defend him. The Doctor warns Mary Jane directly, but in response, she hands the bag of money to the King and tells him to invest it for her. The doctor warns them one final time of the mistakes they are making, and then departs.