It's probably partially true, but very misleading. I've been reading up on some stuff. Apparently, FDNY and NYPD had issues with working together at sites, but you can't say Giuliani did nothing:
In July 2001, Mayor Rudolph Giuliani signed a directive entitled “Direction and Control of Emergencies in the City of New York.” Its purpose was “to ensure the optimum use of agency resources while … eliminating potential conflict among responding agencies which may have areas of overlapping expertise and responsibility.”
The directive designated, for different types of emergencies, an appropriate agency as “Incident Commander.” The Incident Commander would be “responsible for the management of the City’s response to the emergency.” The role of the Mayor’s Office of Emergency Management was supportive, to “coordinate the participation of all city agencies in resolving the event,” and to “assist the Incident Commander in his/her efforts in the development and implementation of the strategy for resolving the event.”
Later on in the commission, you read they used that training.
The FDNY response began immediately after the crash.
Joseph Pfeifer, Deputy Assistant Chief, FDNY: Right from the beginning, before we even arrived at the Trade Center, what you see is the beginning of an Incident Command System, where things are placed in order, and command is taken immediately.
Mr. Pfeifer (on 9/11): “We have a number of floors on fire, it looks like the plane was aiming towards the building. Transmit a Third Alarm. We will have a staging area. Vesey and West Street—have the Third Alarm assignment go into that area—Second Alarm assignment report to the building.”
Mr. Pfeifer: So from the bullet point when the plane hit the building, we started our Incident Command System.
The chiefs were doing their job, but it seems as though the officers/firemen weren't well trained with how to respond to Incident Commanders.
Somebody did screw up with the repeater system though. It wasn't automatic and the chiefs didn't know how properly use them.
At 9:05 a.m., two FDNY chiefs tested the WTC complex’s repeater system. This was the system installed after the 1993 bombing in order to enable firefighters operating on upper floors to maintain consistent radio communication with the lobby command. The system had been activated for use on portable radios at 8:54 a.m., but a second button which would have enabled the master hand-set was not activated at that time. The chief testing the master handset at 9:05 a.m. did not realize that the master handset had not been activated. When he could not communicate, he concluded that the system was down. The system was working, however, and was used subsequently by firefighters in the South Tower.