I saw your post a few days ago and was intrigued by it. I live in the general area of these places and one of my hobbies is trying to find people in the general area that I think may have Cherokee ancestry.
What I'm about to say is unproven conjecture on my part.
In the 1860 Census for Franklin Co, TN, there is a four year old Joseph Hill. He appears to be living with his mother, Lucinda Hill, in the household of Nancy Barnes b 1805, NC. There are two other Barnes' in the household; ages 14 and 16 (or 11). You could assume that Lucinda is the older married daughter of Nancy making her Lucinda Barnes. No clue of the father of Lucinda and the husband of Nancy. I noticed that there are one or more Lucindas later on.
The area is around Cowan, Franklin Co, TN. I don't know the history of the Cowans but know enough to say that they were huge land owners. The census indicates that one Cowan was worth $20,000 not including his land holdings. The Hills were probably share croppers. A series of mountains run more or less along the TN AL border with a series of coves stretching north to south into AL. These coves include Paint Rock, Sinking, Big Coon, Jefferies, McMahan, etc. The Cherokee relinquished more territory in 1817. Alabama became a state in 1819. Before the ink was dry on the treaty, white settlers came across the mtns to settle the coves. Today, north and south highways such as 56, 16, and 97 lead from TN into AL. It was natural and understandable that share croppers without land would flood into the new territory.
The is a history center and/or library in Franklin that has family histories. Their hours are such that I am unable to go. But there might be info on the Hills and Barnes there. The family I picked out was poor and the poorer the harder to track.
As to the Cherokee aspect. I think the chances of Joseph Hill being an FBI (full blooded Indian) is nill. Most of the mixed blood Cherokees of any high percentage goes back into the 1700's. By the late 1700's, the Cherokee and the whites hated each other. The removals were in the 1830's and the US Army (Gen Winfield Scott) was charged with the removal. How effective was the Army? Given the level of hatred, I believe they were very effective. I think the whites were very happy to "rat out" anyone with NA blood because their land would become available.
I think most of the mixing occurred during the Indian Trading era and was pretty much over by the time of the birth of the US. I believe that I'm correct in saying that the revered Chief John Ross was 1/8th and that Alexander McCoy, the last chief in George was 1/16th.
Believe me, I've searched for my Cherokee ancestors and there ain't none.
I found the Busby name of interest. Robert busby came to Stewart Co in TH in the early 1800's. At that time, Stewart stretched from the KY line to what would become the AL line in middle to west TN. Some of my families started out in Stewart Co and flowed south into northern AL. This is my first knowledge of Busbys in this TN/AL area. Note for future investigation.
If you don't live in this are, look at googlemaps or mapquest at the area along the TN/AL state line.
Sorry for all of the conjecture and no facts.