Tori Amos has said in interviews that she had two maternal second-great-grandparents who were enrolled Eastern Cherokee. Genealogists have never been able to find the records, but since her statements are more specific than the usual, I thought it was worth pursuing.
I've now gone through all 16 of her second-great-grandparents, and I've found that her ancestry is European. There are a couple points worth double-checking, however:
1) Anderson Jackson Copeland -- his wife and son are listed as white, so that makes it improbable for him to be Cherokee
2) John Akins and Sallie Akins -- as with Jack (above), their son is listed as white, so once again improbable
If anyone is interested in pursuing this, those would be the only points to check; the other 13 are very clearly white. If not, we can assume her family story was inaccurate.