Our Leavell family had a legend about an Indian ancestor, too, and the fact that our Leavells don't grow much in the way of beards and have big noses seemed to fit the stereotypical Indian. But in years of genealogy searching, I never found a single AmerIndian in our line, and one should always be skeptical. For one thing, EVERY family in America claims to have an Indian ancestor, even families who emigrated from Europe during World War II! For another, it's ALWAYS a beautiful Indian princess marrying a male Caucasian, never a big AmerIndian buck who married a blonde little Caucasian, suggesting the family legend is a purely racist one. There are legitimate AmerIndian links to Caucasians, especially to Cherokee tribes, but they are few and far between. Unless you can document it, consider the family legend simply that--a story.
Finally, there IS a Leavell in Warren Commission report on JFK's assassination, but I have no idea what his ancestry is. I read about it in passing, and didn't realize at the time how many Texas Leavells are related to my line, so I didn't write down the details.