Feynman and Gell-Mann, as colleagues, always engaged in low-level one-upmanship. This story from Al Seckel at Feynman Online is a classic:
…I was with both Gell-Mann and Feynman and the subject of kooky letters and phone calls came up. Feynman started relating the story of how one crazy woman called the office about some ridiculous theory of magnetic fields. He just could not get her off the phone.
Gell-Mann responded, “Oh, I remember that woman. I got her off the phone in less than a minute”.
“How’d you do that?” Feynman asked.
“I told her to call you. That you were the resident expert in the topic” said Gell-Mann.