You misunderstand. I am not interested in the specifics, or even generalities, of your family. I started by trying to answer a question you asked and providing you with some insight.
Of course there is nothing wrong with being curious and investigating leads, that is the essence of detective work, the art of deduction, which is what genealogical research is.
I get the sense that you are feeling a little defensive,apparently I have challenged a family story that has taken root. I have not. I know nothing of your family, recall that I asked the name of the outlaw. You never provided an answer, but I found it in the link you provided: Jesse James.
I just offer what little knowledge and opinion that I possess..
As regards claims of Indian ancestry. I remain skeptical of all such claims, it seems that virtually every person in this country, more accurately the south, that has an abiding interest in family history claims Indian Ancestry. My grandmother, born 1882, told me that we had such. I have not been able to verify that, and DNA has not born it out either..so ir remains a family myth.
Complicating the situation more, is that the vast majority of persons who claim Indian ancestry, claim to be Cherokee. I asked myself why that could be, especially for people whose family are of the south of the U.S,A
It turns out that Cherokee are considered by many to be "white Indians", Indian royalty, the most civilized (i.e. most white acting), the number of native American peoples that were obliterated by whites in their movement west will never be known, but very few persons who claim Indian ancestry, will claim to be Saponi, Creek, Choctaw, Fox, Siouxan or any more obscure tribe..