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Washington (CNN) Ben Carson is back -- and so are the controversies and contradictions that have dominated his time in politics.

President-elect Donald Trump this week tapped Carson to run the Department of Housing and Urban Development -- the latest twist in an odd, on-again, off-again relationship between the two former Republican primary rivals.

It will be the first-ever government job for Carson and put him in charge of a massive budget. Important policy decisions, including the integration of public housing outside of struggling, minority-dominated neighborhoods, will be in his hands. And Carson's previous public comments indicate he is deeply skeptical of the agency he would run.

The lone qualification some Trump supporters offered was that Carson brought the first-hand experience of actually living in public housing as a child. Former Arkansas Gov. Mike Huckabee even said House Democratic leader Nancy Pelosi was "racist or just dumb" for suggesting he wasn't up to the job, claiming on Twitter that Carson would be the first HUD secretary to have actually lived in public housing.

Except it wasn't true.

Close Carson friend Armstrong Williams -- who had previously told reporters that the neurosurgeon had lived in public housing as a child -- backtracked Tuesday morning.

"Dr. Carson's mother worked 3 jobs at a time to keep them out of public housing, but he grew up around many who utilized housing programs," Williams tweeted Monday.

It's the latest in a line of questions about Carson's childhood in southwest Detroit.

What's clear: He grew up in a single-parent household with a mother who worked several jobs to make ends meet. They occasionally relied on public assistance, including food stamps, and made several moves before landing in what Carson has described as an "upper-lower-class neighborhood."

There, he began an improbable rise that led him to spend nearly three decades as director of pediatric neurosurgery at Johns Hopkins University. Carson wrote several books and inspired the Cuba Gooding Jr. movie "Gifted Hands."

But he has also described a violent youth, fueled by anger. Carson told stories of attempted stabbings, brick-hurling, rock-throwing and more. He wrote in his "Gifted Hands" autobiography that he'd attempted to attack his own mother with a hammer in an argument over clothes.

But nine friends, classmates and neighbors who grew up with Carson told CNN last year they have no memory of the anger or violence the candidate has described.

Trump had ferociously mocked and ridiculed Carson over the stories about his youth while on the campaign trail. Trump once likened Carson to a child molester, said his anger was pathological and once even grabbed his own belt buckle to skewer Carson's claim that he attempted to stab someone once but was thwarted by hitting the person's belt.

"How stupid are the people of Iowa? How stupid are the people of the country to believe this crap?" Trump asked.

With Ben Carson wanting to hit his mother on head with a hammer, stab a friend and Pyramids built for grain storage - don't people get it? — Donald J. Trump (@realDonaldTrump) November 6, 2015

That tension seems to be receding, as the bigger question becomes whether Carson is prepared to lead an agency with a budget of $45 billion and a staff of 9,000.

Is Carson qualified?

Democrats have praised Carson as a brilliant brain surgeon, but said he has no experience with housing policy.

"I have serious concerns about Dr. Carson's lack of expertise and experience in dealing with housing issues," incoming Senate Democratic leader Chuck Schumer said in a statement. "Someone who is as anti-government as him is a strange fit for Housing secretary, to say the least."

Pelosi, meanwhile, called Carson "a disconcerting and disturbingly unqualified choice."

The Trump transition team didn't respond to a request for comment on this story.

Vice President-elect Mike Pence touted Carson as a "brilliant man" in an interview on "Fox and Friends" Tuesday morning.

"He's an extraordinarily humble man. He grew up in Detroit. He grew up in an urban environment and built a life story that's been an inspiration to millions of Americans. He's going to lead that agency with integrity, with great distinction," Pence said.

But even Carson himself has questioned his ability to run massive government agency.

"Dr. Carson feels he has no government experience, he's never run a federal agency. The last thing he would want to do was take a position that could cripple the presidency," Carson's friend Williams said shortly after the election amid intense speculation about a potential Cabinet pick -- before Carson changed his mind and decided to enter the Trump administration.

Will Carson integrate public housing?

Neither Trump nor Carson has laid out specific plans or policy proposals for public housing.

But the first casualty of Carson's installment at HUD could be a push under President Barack Obama to integrate public housing under the 1968 Fair Housing Act.

Carson would have wide latitude to decide whether he agrees with the Obama administration that government should play a role in addressing the forces -- from crumbling inner-city schools to limited access to transportation -- that stem from segregated housing by pushing public housing outside poor, minority-dominated areas and toward wealthier neighborhoods.

As a presidential candidate himself, Carson indicated he sides instead with Republicans who have decried the effort to require communities to assess patterns of income and racial discrimination in housing, as social engineering.

Carson wrote in a 2015 Washington Times op-ed that the requirement would heap pressure on suburbs to abolish zoning rules that keep low-income apartment complexes from being built by limiting multifamily housing.

That would, Carson wrote at the time, "fundamentally change the nature of some communities from primarily single-family to largely apartment-based areas by encouraging municipalities to strike down housing ordinances that have no overtly (or even intended) discriminatory purpose -- including race-neutral zoning restrictions on lot sizes and limits on multi-unit dwellings, all in the name of promoting diversity."

"These government-engineered attempts to legislate racial equality create consequences that often make matters worse," Carson wrote. "There are reasonable ways to use housing policy to enhance the opportunities available to lower-income citizens, but based on the history of failed socialist experiments in this country, entrusting the government to get it right can prove downright dangerous."

Is public housing like communism?

Meanwhile, Carson appeared to compare public housing to communism in a radio interview conservative host Jan Mickelson in the summer of 2015.

Mickelson told Carson that eastern Iowans were being told that they "have to recruit from Chicago their poverty-afflicted individuals to bring them to Iowa in order to qualify for Section 8 Housing."

"This is just an example of what happens when we allow the government to infiltrate every part of our lives," Carson said. "This is what you see in communist countries where they have so many regulations encircling every aspect of your life that if you don't agree with them, all they have to do is pull the noose. And this is what we've got now.

"Every month dozens of regulations -- business, industry, academia, every aspect of our lives -- so that they can control you. And this is exactly what Thomas Jefferson predicted. He said the people would become lackadaisical, they would not be vigilant, the government would grow, it will infiltrate every part of their lives, and it will take over.

"But just before -- just before we become another type of government, the people would wake up. I'm hoping that this is the time when they wake up."