I wonder if you have any further information on Turner's wife or widow?And also if you can cite the 1830 census record?
I agree with your theory.Samuel Bynum's 1790 household had in it two males under 16.In 1800, his sons William and Gray (who were both married by then) are maintaining separate households and Samuel has a male 16-26 in his household.This is presumably Turner Bynum.If so, it would seem to eliminate the possibility that his son was the same Turner Bynum married in Charleston in 1799.This 1800 census suggests that Samuel's son Turner did not marry until after the 1800 census.
In support of your theory, I note that the 1820 Giles County household of Turner Bynum is an excellent match to the 1810 Lincoln County household.The Turner Bynum located a few miles south of Lincoln County in 1820 Richland County is not a good match to the 1810 Lincoln County household, for he had more children than were shown in 1810.(On the other hand there is no other sign of this person in 1810.)
One obvious line of research is in Lincoln County.Turner Bynum was to inherit his father's plantation upon his mother's death.Samuel Bynum's will gives to his son Turner "one negro boy and at his mother's death I give to Turner the plantation lent to his mother."
A record should exist of Turner's sale of this inherited land.However, unless I missed them, I did not find any deeds at all by Turner Bynum recorded in Lincoln County.Obviously, the hope is that a deed might indicate his place of residence.