Hi Ron:
In response to your posting, Davidson County, North Carolina was cut from Green County, NC, which at one time extended to the Mississippi River. The first settlers arrived in Davidson County, NC (Nashville) in 1779 at a time when there were few, if any, white settlers in present-day Middle Tennessee. Davidson County's southern boundaries extended only to the valley of the Cumberland River. The land mentioned was on the Duck River, thus it was farther south and not officially in Davidson County. This explains the "formerly Greene County" notation.
The 1793 deed came during a time when Tennessee was the United States Territory South of the Ohio River, commonly called the Southwest Territory. Congress accepted Tennessee into the United States on June 6, 1796. Rutherford County is a large county, and only part of it was formerly Davidson County.
My little book, "Tennessee Territory to Statehood," may help solve the riddle. It's available from The Overmountain Press, Johnson City, TN. (1-800-992-2691)