Out-of-towners documenting New Orleans pretty much always get race wrong. Filmmakers, newspaper reporters, whatever the medium — it doesn’t matter. They may do wonderful things with Carnival floats or hurricane-whipped palm trees, but they get race wrong.

After viewing a spate of post-Hurricane Katrina documentaries, that was a concern shared by the four out-of-town filmmakers behind a movie that’s an exception to the rule. It’s called “Getting Back to Abnormal,” a raucous and brilliant documentary that PBS airs nationally on Monday as part of its “POV” series. (Don’t miss it.)

Much the most insightful movie about New Orleans since the levees failed, “Abnormal” scans a citywide panorama of recovery issues: the appalling murder rate, whether to tear down and rebuild the public housing projects, equity, race relations. But unexpectedly, it does so through close focus on one quirky political skirmish, the 2010 contest — not for mayor, though Mitch Landrieu has a cameo role — but for the privilege of representing District B on the New Orleans City Council.

It’s the race that pitted a black pastor, the Rev. Corey Watson, son of a failed mayoral aspirant, the Rev. Thomas Watson, against Stacy Head, the white, shoot-from-the-hip incumbent who had recently survived a recall petition after some insensitive emails were unearthed.

In the early going, we are treated to footage that shows Head at her most uppity, rudely sticking a large cardboard poster in front of fellow Councilwoman Cynthia Willard-Lewis during a hearing of the council’s Sanitation Committee.

In the film’s recurring visits to the broadcast booth at WBOK-AM, the black-interest radio station, talk jocks Paul Beaulieu and John Slade smirkily trash Head, calling her “point guard for the ‘shadow government,’ ” a phrase popularized by then-Mayor Ray Nagin. It’s a reference to the political “coup” they see coming as a whiter, though still majority-black, post-Katrina electorate claws back political offices won by African-Americans over the past several decades.

That had happened to the District B seat in 2006, when Head wrested it from Renee Gill Pratt at a time when many black voters still had yet to return to the city. Would she manage to hang on?

Many viewers at this point will settle back (or turn off the TV in disgust), assuming they’re in for yet another intellectually lazy depiction of New Orleans as South Africa or as a slave plantation: a racially bipolar world in which pitiable blacks are ground under the heel of a white elite.

Suddenly the scene shifts and the screen is filled by a gaudy, foul-mouthed, street-smart black woman named Barbara Lacen-Keller. Viewers will be forgiven for assuming that we’re in for yet another round of Head bashing.

But no. Not at all. Lacen-Keller turns out to be Head’s secret weapon, a savvy political operative who believes fervently — as do many black people, according to polls — that Head is not a bigot. Indeed, as the candidate insists on her own behalf, she’s a no-bull---- antidote to a world in which black pastors ride “$120,000 Mercedes” while the suckers in their flock take the bus.

Watson vs. Head: Game on!

Lacen-Keller is a documentary filmmaker’s dream come true, and Head’s pretty outrageous all by herself. Indeed, “Getting Back to Abnormal” is a movie so full of well-exploited lucky breaks that you’re left to wonder at what point the filmmakers junked whatever preconceptions they arrived with and began going with the flow of the marvelous footage they had started to accumulate.

The first preconception that had to be overcome was that the market for Katrina films hadn’t already been tapped out. That another post-K documentary was not only possible but imperative struck the team as they sashayed and strutted in the second line that followed the casket of Michael Smith, the esteemed Louisiana photographer, producer/director Paul Stekler revealed in a recent phone call.

The crazy energy of New Orleans had to be captured, the joy amid grief, the bare-knuckle politics and the notorious corruption, the racism, the sublime and the banal, said Stekler, who runs the University of Texas film department.

But a second line for a deceased photographer doesn’t lead straight to a councilmanic race in Central City. In the early going, Stekler and his buddies — New Yorkers Louis Alvarez, Andy Kolker and Peter Obadashian, of the Center for New American Media — began filming across a wide spectrum of topics, uncertain what to home in on.

They got some great footage from inside the writer’s room of the “Treme” TV series and thought of centering the whole film on the show, Stekler said. Not a frame of that footage made the cut. They toyed for a time with building their documentary around the famous cluster of Lower 9th Ward houses sponsored by Brad Pitt’s Make it Right Foundation. They considered doing a film about St. Bernard Parish, the equally devastated white equivalent of the Lower 9th Ward, a place all but ignored by world media.

Then they met Head and Lacen-Keller — along with Head’s mother, a scene-stealer in her own right — and everything fell into place.

Not to sell the Watsons short. Gospel choirs and call-and-response histrionics from the pulpit make for great moments. In one remarkable scene, the candidate’s father says that church/state rules forbid political endorsements by pastors, then slyly sidesteps his own ban by begging God to “release” the congregation to support his son.

And at full cry, Corey Watson’s theatrics rival anything in Lacen-Keller’s repertoire, as when he climbs up onto the pulpit like a mountain goat and then scales the altar rail while raving that he will reach higher and higher in service to the city.

When it comes to filmmaking, you make your luck, Stekler said. He credits Alvarez as the unseen interviewer responsible for one of the film’s more wrenching moments. A grateful resident of the Columbia Parc public-housing development, formerly the St. Bernard, was talking about the bad old days when she stunned the filmmakers by quietly tallying her own losses to fatal violence: one son, three nephews.

Oliver Thomas, the disgraced former council president once considered a mayor-in-waiting, delivers a mordant comment on New Orleans: a city with a “fest” for everything from jazz to death — everything except an “eliminate poverty fest.”

Stekler, also unseen, gets the credit for that interview. It makes sense that he would be particularly adept in conversation with a politician. Of the four collaborators on “Abnormal,” he’s the one with the closest ties to New Orleans. He worked as a pollster for Bill Jefferson back in the day — before the ex-congressman traded nine terms in the U.S. House of Representatives for 13 years in the Big House.

18 months captured

The filmmakers shot the whole movie in a few months of visits to New Orleans scattered over about a year and a half, Stekler said. The editing took another 18 months or so.

That’s an eternity in politics. Things change. Head began learning how to curb her tongue — at least some of the time — and jumped from District B to an at-large seat on the council in 2012. And she and Beaulieu actually managed to bury the hatchet; she’s a regular and respected guest on his show these days — no longer the focus of his lip-curling scorn.

The film ends with the observation that Head is now perfectly positioned to segue into the mayor’s office in 2018 — assuming “Abnormal” doesn’t stir up residual animosity and derail her career. (Head denies she has anything in mind other than doing the job she’s got.)

She was already neck-deep in the project when it occurred to her that she had been incredibly naïve — or maybe just plain stupid — to cooperate with the documentary. “What could I have been thinking!” she moaned, recalling a period of intense anxiety as the film was being shot. But both she and Lacen-Keller, her director of constituent services, say they’re happy with the outcome. In their view, it’s a testament to grass-roots resistance, a study in electoral defiance of the political machinery that might have kept a candidate like Head from getting any traction in a part of town like Central City.

Aficionados of New Orleans’ chattering class will recognize a lot of familiar faces (or voices) in “Abnormal”: developer Pres Kabacoff, lawyers Tracie Washington and Buddy Lemann, and journalists Bob Marshall, Ian McNulty, Deb Cotton and Stephanie Grace, as well as some street-level personalities such as public housing resident Stephanie Mingo, who richly deserve the wider audience the PBS broadcast will provide them.

Toward the end, this packed 60-minute film even delivers a kind of “Rosebud” moment, an answer to the mystery of why and how Lacen-Keller, wife of the late Anthony “Tuba Fats” Lacen, overcame her own acculturation as a marginalized black woman and began doing everything in her considerable power to keep skin tone, rather than common sense, from being the dominant criterion in the voting booth. It’s a lesson for both sides of the color line, and Lacen-Keller has the street cred to deliver it.

She’s an astonishing asset to this film — and to the strange city it celebrates.