Some families are aware this, some people have heard rumors or stories from family members about Indian background and some are totally unaware of it. Did great, great, great grandma really have a Cherokee parent?
There may be more Americans with Cherokee DNA in them than of other tribes. This is because Cherokees began intermixing with Scottish and other explorers, hunters and trappers at a much earlier phase in American history--much of it in the mid-1700s.
Maybe it is time to consider the depth of our family trees and all of their complex branches and roots throughout time and the development of the human race. Whether Cherokee or other interesting ethnic backgrounds are deep within us, this certainly seems worth exploring.
In this sense, the official and legal definitions of who is Cherokee or part of some other Native American tribe, and who is not, become less relevant.
At least, this presumption is as good as any other. If memories are DNA-based, they should be proportional to any biological characteristic such as "blood." Since no one can measure racial memories, no one can prove otherwise.