From the about:
Mary Randolph, b. at Turkey Island, 1692. Married (1712) Capt. John Stith. Their only son, Rev. William Stith, was president of William and Mary College and historian of Va. He wrote his "History of Virginia" in 1740; died at William and Mary College, 1752. He married (Feb. 1744) Judith Randolph, of Tuckahoe. Mary Stith, daughter of Capt. John Stith and Mary, née Randolph, married Rev. William Dawson, D. D., second president of William and Mary College …
Therefore, Lieutenant Colonel John Stith, III is not her son.
However, this conflicts with notes in the about for Captain John Drury Stith, II
John Drury Stith, was born about 1658 in Charles Cittie Shire (sic), one of the first four "boroughs" in the royal colony of Virginia, the eldest son of Major Stith. … He married Mary Isham Randolph, daughter of the prominent Colonel William Randolph and Mary Royall Isham of Turkey Island. John and Mary had at least the following children; Lieut. Colonel John Stith whom married Elizabeth Anderson, Mary Stith became the wife of Reverend William Dawson of Queen's College Oxford, and Reverend William Stith, became President of William and Mary College.
So, we need to understand more about Lieutenant Colonel John Stith, III & Agnes Stith