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"Some of the best conversations that we've had is around brands, and the importance of brands, and how you grow a brand, and how you remain faithful to what those core attributes of a brand is," Chenault said. "While he is not known for this, I think Warren is one of the true brand experts that we have."
Buffett's Berkshire Hathaway owns a near 15 percent stake in American Express.
"Warren has been with us the longest," Chenault continued. "Warren captures your heart and mind because he's so passionate, so engaged, so authentic. And he wants to win. And so this disarming manner masks this fierce competitor. But he's a real gentleman."
The newest addition to Buffett's portfolio is IBM, with an almost 8 percent stake, according to the big blue chief Rometty. Buffett told CNBC ahead of Saturday's meeting that he bought more shares of IBM in the first quarter, but the exact numbers through the end of March won't be revealed until the Berkshire's quarterly Securities and Exchange Commission filing due around the middle of this month.
Upon being tapped the IBM's first female chief executive in 2012, Rometty said she called Buffett immediately: "I had just been named, and actually had not even been effective yet."
"He couldn't have been more complimentary. And, again, it's all about a business model, and the things that are important, and to steward the company for the long term," she added.
Common among all four CEOs in how they described their relationship with Buffett, the words "privileged" and "honor" came up a lot during the interview, which can be seen in parts on "Squawk Box" Monday morning.
"It's such a privilege to have him be our largest owner at Wells Fargo," Stumpf said. "We want to earn that respect and make him proud."
Buffett often shared his wisdom through humor, Stumpf said. "We were talking about acquisition one time, and I called him. I said, 'You know, there's this certain problem.' And he said, 'Well, you remember cockroaches never come in single parts … if there's one, there's always more than one cockroach.'"
"There were more cockroaches there as it turned out," said Stumpf, who added that he did not go through that particular deal as a result.