DES MOINES — It has become political lore, repeated on cable airwaves and by Democratic campaign consultants, even presidential candidates. In 2008, as the story goes, black voters were uncertain about Barack Obama’s presidential candidacy until he won the Iowa caucuses, after which they rallied around him over the onetime front-runner, Hillary Clinton.

Some Democrats had suggested that a win in next Monday’s Iowa caucuses could have a similar influence among black voters in South Carolina and elsewhere, to the detriment of former Vice President Joseph R. Biden Jr., who leads among African-Americans in polls. But in reality, according to historical polling data and interviews with some advisers from the Obama campaign, Mr. Obama’s political strength with black voters was stronger than many remember — even as Mrs. Clinton was ahead in many polls in late 2007 and early 2008.

The persistence of the narrative that Iowa made Mr. Obama has long irritated some of his advisers, who said that this recollection from 2008 had led campaigns astray since then, discounted the agency of black voters and minimized the robust grass-roots strategy that Mr. Obama’s team undertook in the South.

Cornell Belcher, Mr. Obama’s chief pollster in South Carolina, said internal campaign polling data showed Mr. Obama surpassing Mrs. Clinton among black voters in South Carolina as early as November 2007, and leading throughout the entire state before Iowa voted. Public polling shows Mr. Obama with clear leads among black South Carolina voters through that November and December, with his numbers growing further after the Iowa caucuses.