One of the arguments offered by those opposing the Bowater theory is a family group for John Bowater and Ann Carter. Recall that John Sr.'s 1st wife was named Ann/Anne.
That family is as follows:
John Bowater [b. c1629]
Anne Carter [b. c1628]
John Jr. [c1650]
Ann Bowater died in 1679.
The argument claims that if Mary Bowater [b. 1688/9] belongs to John Sr., then the above family group negates Baldwin's theory. John Jr. and Thomas were immigrants to America. That the Mary above was a sister to the immigrants, would eliminate Mary [1688/9] from consideration as John Sr.'s daughter.
There is a catch! I have found nothing on Mary [b. 1659] beyond that estimated birthdate. [A handful of online trees have conveniently combined her with Mary, wife of James Wright. That would have made her at least 12 years James' senior, having children well into her 50s and dying at about age 105.] Mary Bowater [b. 1659] may have died prior to 1688. As a result, John Sr. may have elected to name his daughter born in 1688/9 after both his deceased daughter Mary and after his 2nd wife also named Mary. Giving a child the same name as a deceased sibling [or half-sibling] was quite common at that time.