60 Minutes’ Mike Wallace was known for his hard-hitting interviews, never letting his subjects off the hook no matter how much they squirmed. It wasn’t any different when Wallace put late-night legend Johnny Carson in the hot seat. In fact, Carson pulled the plug during 60 Minutes’ first attempt at a profile, only to relent and try again two years later in 1979.

Even then, the comedian couldn’t understand why an investigative journalist would want to interview him. “Why are you doing this?” he asked Wallace. “I’m not running a boiler room operation. I have no phony real estate scam. I’m not taking any kickbacks. I did steal a ring from Woolworths once when I was 12 years old.”

While Wallace insisted that Carson was chosen because he was a national treasure, the interviewer still found ways to make the Tonight Show comic uncomfortable. He confronted Carson with “stereotypes” associated with him — shy,...