I think you're the one being overly pedantic if you only qualify 100% Native American as "American". This country isn't just some economic zone that people come to and from for the purposes of commercial or business activity. If that's all it was, then a much more lax or liberal immigration regime would make perfect sense.
>but the population of the United States is 97.9% not from this continent.
This would be a surprise to the 85% of us who were actually born here. In its most simplified form, what those of us who are skeptical of the current immigration regime are wondering out loud is if these processes do actually make "people born in America" better off. "Immigration is always good" has been the mantra since, as you speculate, the 1960s. Probably worth evaluating that idea from first principles from time to time.