Native American societies were quite sophisticated. Some were closer to anarchy, some weren’t. A lot of what we would like to know got wiped out before any European met them; initial contact was towards the south, but disease spread northward before Europeans did. The writings we do have about their society come from Europeans, which is hardly the best source.

What we can gather from archeology is that they had cities just as big as European ones at the time, and had trade and agriculture on the same level, as well. North America was a fully anthropogenic environment–altered to be better for humans–and the common perception of “vast, untouched wilderness” comes from the fact that Europeans were visiting a century after disease had ravaged the native population.

For example, I’d argue that American Indians were living in something much closer to anarchy than anything else when the technologically vastly superior Europeans arrived with guns and absolutely demolished them.

I disagree. The native Americans were “technologically” quite advanced when it came to stewardship of the land. Think agriculture (food and forests), language and the like. Europeans basically enacted biological warfare on them.

American Indians were mostly killed by the germs that the European invaders accidentally brought. In actual battles the Europeans didn’t fair so well as they were usually vastly outnumbered and the Europeans that defected or got captured mostly preferred to stay with the Indians afterwards. And yes, never trust history written by the winners.