That's an urban myth....albeit, it exists in my family too.
DNA tests I've done on my extended family shows it to be false...at least in my family.
The DNA haplogroups in my family are all European, R1b, U5a, V and H.
I've "met" several third and even fourth cousins online, and one of our very early Americans could potentially have come from one the Quaker communities, or perhaps from somewhere in the Caribbean, very probably from New Sweden, but with no documentation, he could be a Huguenot or German or Irish or English or Scottish or Scotch Irish.... indeed, almost anything, from almost anywhere.
Secondly, since so very few people have had their DNA done, I've no idea where the '80% of old Americans have a Cherokee ancestor' meme originated, but I've come across it quite a few times online. I had no idea it was an urban legend.
Thank you blam.