One day in the summer of 2010, Barry Mills, the president of Bowdoin College, a respected liberal-arts school in Brunswick, Maine, met investor and philanthropist Thomas Klingenstein for a round of golf about an hour north of campus. College presidents spend many of their waking hours talking to potential donors. In this case, the two men spoke about college life—especially "diversity"—and the conversation made such an impression on President Mills that he cited it weeks later in his convocation address to Bowdoin's freshman class. That's where the dispute begins.

In his address, President Mills described the golf outing and said he had been interrupted in the middle of a swing by a fellow golfer's announcement: "I would never support Bowdoin—you are a ridiculous liberal school that brings all the wrong students to campus for all the wrong reasons," said the other golfer, in Mr. Mills's telling. During Mr. Mills's next swing, he recalled, the man blasted Bowdoin's "misplaced and misguided diversity efforts." At the end of the round, the college president told the students, "I walked off the course in despair."

Word of the speech soon got to Mr. Klingenstein. Even though he hadn't been named in the Mills account, Mr. Klingenstein took to the pages of the Claremont Review of Books to call it nonsense: "He didn't like my views, so he turned me into a backswing interrupting, Bowdoin-hating boor who wants to return to the segregated days of Jim Crow."

The real story, wrote Mr. Klingenstein, was that "I explained my disapproval of 'diversity' as it generally has been implemented on college campuses: too much celebration of racial and ethnic difference," coupled with "not enough celebration of our common American identity."

For this, wrote Mr. Klingenstein, Bowdoin's president insinuated that he was a racist. And President Mills did so, moreover, in an address that purported to stress the need for respecting the opinions of others across the political spectrum. "We are, in the main, a place of liberal political persuasion," he told the students, but "we must be willing to entertain diverse perspectives throughout our community. . . . Diversity of ideas at all levels of the college is crucial for our credibility and for our educational mission." Wrote Mr. Klingenstein: "Would it be uncharitable to suggest that, in a speech calling for more sensitivity to conservative views, he might have shown some?"

After the essay appeared, President Mills stood by his version of events. A few months later, Mr. Klingenstein decided to do something surprising: He commissioned researchers to examine Bowdoin's commitment to intellectual diversity, rigorous academics and civic identity.