"Most people know Joe Biden's character. They know his value system. They know that he visited Iraq and Afghanistan over 21 times as a United States senator and vice president," Brazile said on "The Five." "But this story -- the way it came across and it came out -- [was] heartfelt because people know that Joe Biden is heartfelt."
Biden responded Thursday to a Washington Post report claiming that a military story he'd shared on the campaign trail "never happened," saying in a podcast interview: "I don't know what the problem is."
The anecdote in question came up earlier this month when Biden recounted a story he claimed to be "God's truth" at a campaign stop in New Hampshire.
The Washington Post says it appears as if Biden "jumbled elements of at least three actual events into one story."
Co-host Lawrence Jones criticized Biden for the perceived blunder, saying that he either has a memory problem or is lying.
"So the campaign realizes, the people that are brought to protect Joe Biden, that there is a problem going on whether it's memory or whatever it may be or he's just lying and they don't want him out there," Jones said.
Brazile disputed Jones, insisting that Biden "misspoke," unlike President Trump, whom she said "lies."
Fox News' Joseph A. Wulfsohn contributed to this report.