Maybe a note of the possibility should be included on your "Tree".
My father swears his mother was part Indian, her brother was nicknamed "Chief". I can not find any "proof", but I have noted the "rumor".
There two other reasons why you should not discount the possibility, a lot of men married after they arrived in America. Who did they marry? Native American women is the most likely answer. And don't foreget that if a Native American could get by claiming to be white on the Census, they did!
Do a DNA test do be sure!