"We have no idea how he died in the towers," says Al Regenhard, a retired police officer whose firefighter son, Christian, was killed on 9/11. Regenhard identifies himself as a Republican who voted for Giuliani.
"We haven't recovered his remains, so we don't have any information."
Such claims are potentially damaging to Giuliani, because he has built his campaign upon his perception as a strong leader who capably led a city through a tragedy.
Without 9/11, Giuliani almost certainly wouldn't be a serious presidential contender, and he uses his experience on that day to make the case that he understands the stakes in the war on terror.
The Giuliani campaign takes issue with each of the claims made in the ad. They argue that the failure of some fire radios was inevitable on 9/11, given the clogged communication channels and the large volume of concrete and steel at the World Trade Center.
Operations to recover firefighters' remains were abandoned earlier than some firefighters wanted out of concern for their safety, the former mayor's camp says. And his decision to put the Office of Emergency Management in the World Trade Center complex was based on advice offered by subordinates, said Howard Safir, who served as fire commissioner and, later, police commissioner when Giuliani was mayor.
"He got bad advice, and relied on some people who appeared to have the expertise, and they did not," Safir said. "I believe it was a mistake, but it was in good faith."
Giuliani has defended his decision on the emergency management center by noting that it was chosen in part because of its proximity to the New York field offices of key federal agencies, including the FBI, the CIA and the Secret Service.
Safir said Giuliani was always supportive of the needs of firefighters, citing his decision to free up $10 million so the department could purchase fireproof gear early in his tenure as mayor.
"This is politics -- it's mostly nonsense. The fact is that nobody's a better friend to firefighters than Rudy Giuliani," he said. "When I go around the country and talk to firefighters -- not union officials -- they love Rudy. Union leaders are not firefighters. Union leaders are politicians."
Schaitberger, the union president, said his union is nonpartisan.
Though the union leans distinctly toward Democrats -- as do most labor organizations -- the IAFF sends about a third of its political donations to Republicans, Schaitberger said.
In last year's elections, the union supported Republicans, including Florida Gov. Charlie Crist, former New York Rep. John Sweeney, and former Pennsylvania Rep. Curt Weldon.
Local fire unions in New York endorsed Giuliani in his two successful mayoral runs, in 1993 and 1997, though the unions' relationship with Giuliani soured amid contract disputes late in this tenure as mayor. Some 12,000 New York City firefighters are represented nationally by the IAFF.
Though some critics have compared the IAFF's attacks on Giuliani to the Swift Boat Veterans for Truth's broadsides against Democrat John Kerry in 2004, Schaitberger said he had been careful not to stretch facts.
"You know the difference? Everything in our video is accurate and the truth," he said. "If it has the same effect, so be it. Frankly, it's my hope."