The web site that you cite does contain interesting information, though little primary or original research.As one example, he is too quick to dismiss the Winthrop-Colver connection.I've not read a genealogist, yet, who claims to have proven that Mary Winthrop married John Colver.Few discount the possibility, however, because there is simply too much anecdotal evidence. One example, from "Historic and Descriptive Sketches of Groton" (by various writers local to the area, but compiled and copyrighted 1909 by C.F. Burgess:
Sketch titled "Oldest Baptist Church in the State" and dated 1838(page 97):
"The church was blessed with faithful laymen as well as officers .Joseph Colver, a lineal descendant of Gov. Winthrop of Connecticut, was a judicious and trusted helper, and a tower of strength to the church in his day and in faithful attendance his record is without parallel.He carefully kept a diary and according to its pages he was absent from Lord's day services only twice in forty years.Two of his grandsons have filled important positions in the Baptist ministry, Rev. Palmer G. Wightman whose name appears later as Pastor of this church, and Rev. Joseph C. Wightman an eminent scholar and divine."
Two things are striking to me regarding the Winthrop connection:Joseph was very few generations removed from John.So few, in fact, that it would still have been a matter of oral family history that would have been well accepted.Second, this was written more than 100 years closer to the fact, was evidently a claim that he made about himself and was accepted by others.
This is among the many things that I've read that make it impossible for me to dismiss the Colver-Winthrop connection and to hold out the possibility that John Colver married twice.