The traditional ancestry of John Sturges is that he was the son of Edward Sturgis of Yarmouth who was the son of Philip Sturgis of Hannington, but this has been shown to be false by Roger Faxton Sturgis in his book "Edward Sturgis of Yarmouth, Massachusetts 1613-1695 and his Descendants". Briefly, In his will dated May 26, 1618, Philip Sturgis left lands in West Haddon to his son Edward. Edward was his first son by his first wife, and therefore would have been born about 1600; the third child, first from the second marriage, was born in 1608. Edward of West Haddon married Alice and had 4 children: Alice (1619), Mary (1621), Edward (1624), and Rebecca (1626). According to a tablet erected in All Saint's Church in Holdenbury, Alice Sturgis the wife of Edward Sturgis died January 20, 1659, and her husband Edward Sturgis of West Haddon died there on October 22, 1670.
Edward Sturgis of Yarmouth, however, emigrated to Charlestown in 1634, and married Elizabeth Hinckley about 1639. They had 7 children until about 1652. Elizabeth died on February 14, 1691, and in April of 1692, Edward Sturgis of Yarmouth married Mary _____. He died in Yarmouth in October of 1695.
Edward Strugis of Yarmouth mentions only his son Thomas in his will of 1695 implying that all his other sons are dead. Since John Sturges did not die until 1700, he could not be Edward's son.
Also, Edward Sturgis of Yarmouth would have to have been about 95 years old when he died which his highly unlikely for the period, though not impossible.

Update:

[...] received a partial copy of "The Sturges Family Story" by Arthur Danforth from Neil Zaccari in June of 2008. Unfortunately the sources were listed in the appendix and were not scanned by him. The book was hand typed and found in the Daughters of the American Revolution [Library]. The book supports the claim that John Sturges is the son of Edward of Yarmouth, but makes the following statement:

"There is some dispute whether John was a son of Edward or a brother or a nephew; Amos Otis, the historian, believes and the preponderant opinion seems to be, that he was a son."

He also makes the following statement which would be necessary to connect the two Edward's together as one married an Alice and the other Elizabeth Hickley.

"Edward married Alice or Elizabeth Hinchley"

It is increasingly clear to me that the ancestors of John and Edward Sturgis are not known, and are more than likely not Philip Sturgis of Hannington who was the father of a different Edward Sturgis.