Yes, that was one group headed up by union bosses who may well have been politically motivated...as the part in the wiki article that you failed to post goes on to say.
"The Giuliani campaign stated that the union was politically motivated from tough contract negotiations from Giuliani's second term as mayor and quoted a retired firefighter, Lee Ielphi (a father of 9-11 victim who was called to duty as a firefighter that day), saying "Firefighters have no greater friend and supporter than Rudy Giuliani." The union denied political motivation for the criticism.[23] Jim Riches, an official at a firefighters' union and the father of a fallen Ground Zero firefighter, said, "We have all the UFA, the UFOA, and the fire members are all behind us -- the International Association of Fire Fighters.... And we’re going to be out there today to let everybody know that he’s not the hero that he says he is." The unions' complaints focus on the malfunctioning radios used by the fire department on September 11, 2001 and what they claim was a lack of coordination at the Ground Zero site.[24]
In response to this image, Giuliani stated at a presidential debate that he "...would like people to look at my whole record. Long before September 11, 2001...the reason that I believe I'm qualified to be president of the United States is not because of September 11th, 2001. It's because I've been tested...and I got very, very remarkable results. And that is the evaluation of other people, not me."
And you look at the crime rates that went down, the feeling of security that NYC still enjoys since his tenure, the esteem of Americans for NYC residents after 9/11 and their response under his leadership... compared to what it was before. I would say most of us out here had a very low opinion of many New Yorkers from previous conversations and experiences up to that point... then they impressed the hell out of the rest of us.
And don't get me wrong, I always kinda liked Koch.