This seems like a huge generalization to make about the hundreds of cultures inhabiting North America from the time of the European arrival to the beginning of the 20th century (the period and location the speaker seemed to refer to). It certainly fits with the stereotypes propagated about Native Americans in the 20th century. But is it true? The Lakota, for instance, seemed very aware of their physical territory, based on their policy and storytelling. Did they really not see it as having borders?
I can say that between the Creek and Choctaw in South Alabama this was not true. In Clark county, AL there is a ridge that runs north and south located between the Alabama and Tombigbe rivers. This was the boundary between these tribes. They maintained about a 100 yd open area that ran the length of the ridge, that way hunting parties could easily tell when they approached the border. Each year both tribes met in the early spring and walked the boundary cutting down any saplings to maintain the boundary.
When whites showed up this open ridge was some of the first land they settled (It was already cleared)
I think the more nomadic tribes of the Great Plains would probably not have really had borders, or cared much about them. For example, I know the Comanche tribes were known to range for thousands of miles.