Ben Carson didn't live in public housing

As politicians squabbled over Ben Carson's qualifications for secretary of Housing and Urban Development, one story surfaced about the retired neurosurgeon's upbringing.

One of Carson's biggest strengths, some argued, is that he lived in the very public housing projects he would be overseeing if confirmed to lead the department under Donald Trump's administration.

The president-elect tapped his former primary rival for the position on Monday. When House Democratic leader Nancy Pelosi called Carson "unqualified," former Arkansas Gov. Mike Huckabee defended Carson, pointing to his upbringing.

Except, Carson didn't grow up in public housing.

Armstrong Williams, a conservative talk show host and longtime advisor to Carson, tweeted on Monday that Carson avoided public housing thanks to his mother, who worked three jobs at one point.

Prep for the polls: See who is running for president and compare where they stand on key issues in our Voter Guide

Williams did tell NPR that Carson grew up in subsidized housing, which are homes owned privately but paid for with public subsidies. Williams said it was Carson's experience "life growing up in subsidized housing, growing up in poor communities" that helps him understand housing programs. And, he added, Carson's work in medicine has helped him understand the health problems afflicting Americans who use these housing programs.

"His medical career has given him an extreme foundation," Williams said. "And also he's never been disconnected from these inner cities and these people who live these lives."

Carson grew up in Detroit. His mother and father divorced when he was young, though records obtained by the Daily Mail contradict some details Carson has given about his parents. Without his father, Carson and his family moved to Boston to save money. There they lived with Carson's aunt and uncle in two different homes, the Boston Globe reported.

Huckabee tweeted a mea culpa, but not without taking a swipe at the New York Times, who had reported that Carson lived in public housing. The Times issued a correction on the story online, saying the error was based on information from Williams.