I have a friend with North African ancestry (mother is Spanish) and neither of her sisters show the same (all with 23andme).
At that distance, it's entirely possible you have the ancestry claimed and the ancestry discovered, but the DNA which would show it is absent for your Native American ancestry.
Good point. You're right -- it's possible. I don't think any of my other family members have gotten analyzed. That would shed more light on the situation.
Edited to add: well, look at it this way. If one were part African in Alabama in the 19th century, one would be well advised to claim to be part Cherokee, if one's coloration and features were such that one could get away with it. Given that, I think Occam's razor inclines me toward the possibility I suggested.
At that distance, it's entirely possible you have the ancestry claimed and the ancestry discovered, but the DNA which would show it is absent for your Native American ancestry.