Thanks for posting. I don't know nearly as much about my ancestry as you do of yours, though I haven't particularly looked, but I too grew up with the tale that I had some Native American ancestry, 8 generations back in my case. 23andMe, however, says I'm .4% African, and, like you, 0% Native American. Since .4% is exactly what you'd expect after 8 generations, I think it's the same kind of situation.

Ironically, I recall my mother's father, now long dead, as being rather virulently racist, but in retrospect it seems likely he's the one my African ancestry came through.