(CNN) -- Some supporters of President-elect Donald Trump have praised his choice of Ben Carson to lead the Department of Housing and Urban Development, noting that the retired neurosurgeon had lived in public housing himself.

Except he didn't.

Former Arkansas Gov. Mike Huckabee, in an attack on House Democratic leader Nancy Pelosi Monday, inaccurately claimed that Carson lived in "government housing."

"Ben Carson is first HUD Sec to have actually lived in gov't housing. Fancy Nancy Pelosi says he's not qualified; is she racist or just dumb," Huckabee tweeted.

The New York Times issued a correction Monday after saying that Carson aide Armstrong Williams originally told the paper that Carson was raised in public housing.

"Using information from a close friend of Ben Carson, the nominee for housing secretary, an earlier version of this article misstated that Mr. Carson spent part of his childhood in public housing," the Times wrote. "The friend, Armstrong Williams, said Monday that Mr. Carson had never lived in government housing."

Carson has said he was raised "in the ghetto" and "in dire poverty."

"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.