It's funny you should mention this, as I saw the documentary and I seem to remember some North American indigenous tribes refusing to participate. Their reasoning was the Nat Geo was just trying to prove they were immigrants like everyone else.
It's primarily because many American tribes try to maintain religious beliefs in conflict with an immigrant identity. Although, evidence points to most of the earliest American humans immigrating across the Bering Land Bridge ~20,000 years ago. The religious stories tribes tell depict that they came from American caves, soil, water sources or other nature-related points of origin.
It's religious-based denialism, no different than what other major religions do when their beliefs conflict with reality.
Except it's no longer 1610.