Here is my critique of the criteria of civilization:
1. Agriculture. Makes sense.
2. Urban Settlements. Highly correlated, but I can see reason for making exceptions. Thomas Jefferson posited as an ideal a largely agrarian based society. Of course, even Jefferson would have probably conceded the need for some "urban settlements." Also, what exactly constitutes an "urban settlement"? I am not an expert on the Iroquois, but I would guess that they had villages that some would call "urban settlements". Maybe not like the grand cities of Europe, or ancient cities of the Americas like Teotihuacan, but settlements where collections of people lived.
3. Monumental Architecture.Highly correlated, yes, but as a condition of being considered "civilized"? Seems somewhat arbitrary.
4. Writing (or its analogues like Incan quipu). Yes, this makes sense. After all, it is hard to imagine a civilization sustaining itself through time and heavily influencing the future when it does not even have a basic system of writing in place. At the bare minimum, it would need to interact with cultures that do have a system of writing in place. That is why the Iroquois had such an influence, because of their interactions with Americans of European descent who had a well developed system of literacy in place. Still, it is valid to note the absence of such a system among the Iroquois themselves.
5. Social Inequality. I would think a criteria like "division of labor beyond that based on gender" would make more sense. Especially if one is going to make judgments about something being "wrong" about a society. Absence of "social inequality" can very well lead to questions about what is "right" about a society. Why did such a society avoid the decidedly negative attribute of having "social inequality." After all, if we are to look at Marxian schemes of classification, the most advanced is communist in which social inequality all but disappears, or at least is rendered irrelevant since resources are distributed "according to need".