A bit of both. There was a lower permanent population density before white settlement which is an important factor. However, historians have shown that many tribes did not have the same consumption and land use beliefs and behaviors as Europeans. Each tribe had its own practices as well. Additionally, there is the myth that the Native Americans lived in a pristine environment when Europeans arrived. Scholars have debunked this concept.

Check out these books for more on this topic

Changes in the Land by William Cronon The Ecological Indian by Shephard Krech The California Indians and their Environment by Kent Lightfoot The Destruction of the Bison by Andrew Isenberg

I know you are asking specifically about Northern Amerindians, but I found out that in South America the portrayal of Amerindians as "one with nature" was not completely fictional. I've read a book called Urutopiag by native Brazilian author Yaguarê Yamã. Modern thought influences in his writing are obvious, but still, the way he depicts Amazonian (?) mythology really makes a point that Brazilian Indians always had a different relationship with nature than Europeans had.

For example, "respecting the nature" happens in many ways. You shouldn't hunt excessively because that would anger a benign deity, Ga'Apy'Hog. However, speaking loudly while in the forest would anger evil demons, the Ahiãg, who will torture human beings gruesomely. Finally, you should not hurt the wild animals that are protected by your spirit guardian; however, you should hurt the animals that are protected by the spirit which antagonizes your guardian. Enraging your guardian will make crossing the woods much less safe, as you won't be protected against the Ahiãg, or maybe even a spirit guardian might try to hurt you.

It's clear that what Yamã presents as "Amazonian religion" isn't the original thing people had in the 16th century. For example, it's full of mythological beings of Guarani (who used to live in the Atlantic shore an in Argentina/Paraguay) culture like the Kurupyra, and it sometimes uses the Nhengatu language which is an artificial language created by Jesuits. Still, seems fair to me to say that the notion that you should respect nature so that demons won't torture and rape you isn't an Westernized concept.

The origin of the belief itself needs to be addressed; it can't be said to originate in pop culture because the concept of "the noble savage" is quite old in western tradition.

Native American tribes from the east coast of North America, upon which much of the "one with nature" ideals seem to be based, used nature to suit their needs.

First, tribes such as the Powhatan, who lived near Jamestown, did not store much food for the winter because they required the hard winter months to keep the population of their tribe in check. If they grew too big, they would have to move, so the hardships of nature kept their size sustainable.

Second, many tribes cultivated the environment around them very carefully. What many colonists saw as rich, abundant nature, was actually a controlled environment a tribe had made. Think about the forest as a garden: you have certain plants in certain areas to attract certain animals, you have burned the trees in one area to allow new growth, and in other places you are cultivating edible vegetables. From a european perspective, this was a more "one with nature" way to sustain yourself in your environment, but it was definitely controlled.