The Times also ran a story about this, and I feel it shows Dean's thought process well.
Some excerpts:
He said that his main mistake had been not immediately condemning the flag during the debate, and that he had decided to change course as he came to understand that his comments had been personally offensive to two of his rivals, the Rev. Al Sharpton, who is black, and Senator John Edwards of North Carolina.
<snip>
Even an hour before his Cooper Union appearance, Dr. Dean said he was unsure how or when he would address the flag issue. In addition to President Carter, Dr. Dean consulted yesterday with the Rev. Jesse L. Jackson, as well as several African-American labor leaders and elected officials.
<snip>
"You can blame the media or blame my opponents, but the fact is, I've got to own my own words," Dr. Dean explained yesterday evening in Manchester. "And that's what I decided at about 3 o'clock this morning."
From "In a Jam, Dean Apologizes"
http://www.nytimes.com/2003/11/06/politics/campaigns/06DEAN.html?pagewanted=1&th