What is the joke, I don't get it either.
There isnt any joke.
That quote "I'm not a pilot, but I did stay at a Holiday Inn Express last night" is from an old Holiday Inn Express Hotel commercial. They were saying that staying at a Holiday Inn Express is a smart choice. So... if a person who stays at a Holiday Inn Express is a smart person, then they could possibly be a doctor...
Hence...
"I'm not a doctor, but I did stay at Holiday Inn Express last night"
Does that clear it up for you?