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The Mayo Clinic knew it had made a sweet deal by securing TV’s most acclaimed documentarian for a speaking engagement in exchange for a free physical. But the notion that that swap would lead to a place in Ken Burns’ oeuvre was just short of science fiction.

“It’s like little boys wishing for a bicycle at Christmas, even if there’s no chance of getting one,” said Mayo CEO John Noseworthy in a phone interview last week from New York, where he was wrapping up a publicity tour for “The Mayo Clinic: Faith-Hope-Science.” The two-hour film premieres Tuesday on PBS stations across the country. “I’m the little boy who got his wish.”

On paper, a documentary about a Midwest clinic may seem too trivial and limiting to attract the attention of someone heralded for his epic takes on the Civil War, jazz music, the national park system and the Roosevelt dynasty.

But mortality is clearly on Burns’ mind these days, and not only because the ever enthusiastic filmmaker turned 65 this summer.

“None of us get out of this alive,” said Burns, still looking like a professor’s teaching assistant as he dug into oatmeal and over-peppered eggs in the lobby of a St. Paul hotel recently. “All of us are super-curious about our health. But focusing on a place that deals with it super-well, it reminds you that maybe we’ve ceded the health care debate to those who don’t know a damn thing about it, and that’s politicians on both sides.”

Burns clearly hopes the film will convince viewers that Mayo’s nonprofit business model will inspire other institutions to follow suit. When he gets revved up about the subject, it’s with the same fervor he used not so long ago to pitch the story of how Jackie Robinson broke the major leagues’ color barrier.

“Look at TV shows: It’s the doctor first, not the patients,” Burns said. “And if we’re really honest, it’s the hospital administrator looking over the doctor’s shoulder that’s first. And if we’re really, really honest, it’s the insurance companies looking over the administrator’s shoulder. But at Mayo, because the doctors are on salary, they’re not paid for unnecessary tests. They’re predisposed to collaboration. There’s a sense of public generosity and plowing profits back into service. It’s a uniquely American story.”

Salute from McCain

The timing of Burns’ unabashed love letter couldn’t be better for Mayo as it plans major expansions on its campuses in Rochester, Phoenix and Jacksonville, Fla. But administrators had to relinquish editorial control to get Burns on board. Noseworthy saw the finished product for the first time this month, along with more than 5,000 fans, during a free screening at the Rochester Civic Center.

“After sitting in a dark room for three years trying to put together good stories, watching it unfold in front of all those people was the highlight of my career,” said Erik Ewers, who codirected the project with his brother Chris and Burns. “I’ve never experienced anything like it.”

The hometown crowd burst into applause whenever the late Sen. John McCain appeared on screen, lauding the clinic’s doctors for diligence and honesty.

“There’s a kind of courage and peace that’s in the twinkle of his eye that means more now that he’s gone,” said Burns, who also used his time with McCain last year to tape his thoughts on Ernest Hemingway and Muhammad Ali for future documentaries. “I actually believe that for all his heroism and service during his life, he’ll do even more in death to help us hew to the kind of principles that will keep us together.”

Other well-known faces checking into the documentary include the Dalai Lama and journalist Tom Brokaw, who recalls growing up in South Dakota and thinking of the Mayo as a secular temple that all Midwesterners could be proud of.

And you don’t have to be a film buff to recognize the actor providing the voice of Dr. Charlie Mayo, one of the two brothers who carried the altruistic vision of their father, William, over the finish line.

Yep, it’s Tom Hanks, who participated in Burns’ 2007 series “The War” as Al McIntosh, editor of the newspaper in Luverne, Minn.

“After we were done recording, he wrote me a letter on one of his typewriters, saying that he was dreaming of McIntosh and is there more on him?” Burns said. “We had never had anyone ask for more. So we dug deeper into the morgue. That film ends with him recounting a snowball fight on the streets of Luverne in 1945. I’ll start to cry.”

Real star: ‘Midwestern nice’

Despite the big names, the true superstars of “Mayo” are William Mayo, the country doctor who worshiped Charles Darwin, and the Sisters of St. Francis, who initially teamed up with Mayo to aid survivors in the aftermath of tornadoes that ripped across southeast Minnesota in 1883. It’s that partnership, more than anything, that drives the narrative.

“Arguably, the single most important ingredient in the continued success of the Mayo Clinic is this thing we call Midwestern nice,” said Burns, who spent part of his childhood in Michigan. “If we just toss it off, it’s just a label and an unfortunate one, because all regions are complicated and have different sides. But if we push on that, there’s a spirit in W.W. Mayo and his sons about service to others, married with the values of the Sisters of St. Francis, that show the betterment of humanity. That continued in the midst of great technical advances and gigantic social upheaval. You can arrive at the Mayo as just a regular somebody from the Iron Range and the guys there are going to greet you the same way as they greet the Dalai Lama.”

The Ewers were originally tapped by Burns to direct the film for his production company, Florentine Films. But the boss became so drawn to the story that he ended up giving himself a co-director credit. The brothers weren’t surprised. “The Mayo Clinic” fits too neatly into Burns’ wheelhouse for him to stand on the sidelines.

“It astounds me — in capital letters — how Ken’s films come out at just the right time,” Erik Ewers said. “This film looks at the power of women at a time when women weren’t thought of much, and now we’re seeing this surge from the #MeToo movement. Then there’s the indirect statements on the current state of health care. All you have to do is stop and see how relatable these subjects are today. But that’s what history and Ken’s work is all about, learning from our mistakes and successes. His instruction book is right there, if you care to read it.”

Neal Justin • 612-673-7431 • Twitter: @nealjustin

The Mayo Clinic: Faith-Hope-Science

When: 8 p.m. Tue.; repeats 9 p.m. Wed.

Where: TPT, Ch. 2.

See a review in Tuesday’s Variety section.