What we've been hearing here is that the New York City firefighters are upset because they want to be on the scene to find and remove the bodies of their brethren firefighters. Police and officials are claiming that it's dangerous to have so many individuals combing the site while heavy equipment is being used, and Giuliani has expressed concern for their safety, saying that they don't want to lose any lives in this recovery effort. I have not heard any US reports of recognizable human remains being put into dumpsters, as the Guardian article reports. (Ashes may be another story.)
On TV over the weekend, I saw a sound bite of a firefighter's union man, saying that Friday's protest was supposed to consist of a peaceful march followed by a short service, after which the protesters were supposed to disperse. The man was lamenting the fact that some people in the crowd didn't follow the guidelines set down by the organizers of the protest.
I also saw a video clip of the protest itself, where men were talking with one another in a level tone, and trying to calm each other down. Actually, cooler heads seem to have prevailed; out of hundreds of protesters, only 11 or 12 were arrested, and apparently they are being charged only with misdemeanors according to the ABC News website.
Tempers flared. It happens, under far less trying circumstances. But DougR is right: this was only a minor tiff. Major embarrassment, but minor tiff.