Perhaps a letter in his file would be sufficient for paying a prostitute. What happens when a LEO gets a speeding ticket? A ticket for drunk&disorderly? Gets in a fight with their neighbor? (We know what happens when they get in a fight with their spouse - lose their right to bear arms and therefore their job. A felony punishment for a misdemeanor.)

Lying about it is another issue? But why lie? Maybe because the probable punishment for the moralists wouldn't fit the offense. "Off with his head!", as the Red Queen would say.