Well, there is some basis in fact here. The original 5 tribes had a confederacy based at Onondaga that was founded before Europeans got here (when exactly is a matter of debate). It was a representative system in which chiefs from the 5 tribes and from the various clans were specifically appointed to 1 of 50 different slots in the Roll Call of Chiefs at the great Council at Onondaga. Then there was one chief called the Thadodaho who presided "first of equals" over the whole thing.
But to say it was a democracy or even a federal government...mmm...that's pushing it. The Mohawk during the 1650s were continually at odds with the rest of the League, and at one point they were at war with their fellow League members the Seneca. Moreover, when consensus could not be reached between the Five Nations, the central fire would be covered and every nation was, in essence, free to go on its own. It was really much more like a loose version of the Articles of Confederation.
Admiration for some aspects of the Iroquois League is nothing new in American History. They weren't called "the Romans of the West" in the 1800s for nothing....but the degree to which some academics will go to deny--in the face of flat-out documentary evidence--that the Iroquois practiced ritual cannibalism, enslaved conquered peoples, and brutally tortured their enemies is really beyond the pale.
Moreover, there were plenty of European models of representative government for the Founding Fathers to choose from: Rome, Greece, the Italian Republics. The U.S. government is firmly in that tradition. We did not have horns of office, roll calls of chiefs, clan representation, elder brothers and younger brothers, condolence ceremonies between the states, etc. There is no Federal Keeper of the Wampum. ;)
Your source "pushes it" in Volume I, Book I, Chapter I, Paragraph 1.... :-)
League of the Ho-dé-no-sau-nee Or Iroquois By Lewis Henry Morgan, Herbert Marshall Lloyd