It's not entrapment. I don't like it when the FAA does this; I don't find it particularly ethical. However, administrative law is the game, not criminal law. There is no miranda. FAA inspectors are not law enforcement officers and not cops. You don't have the same rights you might expect under criminal law, or under that process of law.
The context of your description almost sounds like an inspector who really did want to get to Wyoming, and congratulated the pilot as a way of backing out when the pilot wouldn't go for it. That's also possible, albeit hopefully unlikely.
Inspectors and security agents are routinely sent undercover on airfields to purposely breach security. Teams travel around the country wandering on ramps, waiting to see if people question their identy or call security. Failure of any badged individual to do so can net a fine into the thousands of dollars. It happens every day; a mechanic or lineman can get caught just as easily as a pilot.
Your friend did well.