This is the source of the current information:
William Sargent, the immigrant ancestor, was born in England, about 1600. The latest investigation points to the probability that he was theWilliam Sargent who was baptized in the Abbey Church, Bath, England, June 28, 1606, son of Richard and Katherine (Stevens) Sargent. There is a tradition that William was born in 1602. As the father-in-law of Sargent, Quartermaster John Perkins, came from Bath, it is probable that this record belongs to the immigrant, William Sargent, of Salisbury, Massachusetts.
This is from :William Richard Cutter, Genealogical and Personal Memoirs Relating to the Families of Boston and Eastern Massachusetts, Volume 2, (Boston: Lewis Publishing Co., 1908) 863.
Cutter also mistakenly places John Perkins from Bath instead of HIllmorton. Clearly Anderson is the better choice.