For many years, the specious claim swirled around the internet that Mary was the daughter or sister of Westerly founder Hugh Mosher. Anderson's Great Migration vol. 5, page 104, explicitly rejects it: "Many secondary sources state that the wife of John Maxon was Mary Mosher, sister of Hugh Mosher who married Rebecca Maxon. No evidence has been found for this claim."
It's so old and been so debunked that I was quite surprised to see the "Mosher" LNAB on her profile here. She's currently attached to Nicholas Mosher and Lydia (Maxson) Mosher with an authoritative-sounding biography and long list of secondary and tertiary sources.
WikiTreer Dale Scott in the comments on Mary's profile did a heroic job of wading through the sources cited as "evidence" for Nicholas & Lydia as Mary's parents and he shows that literally none of them even attempt to link her to those parents—most are weary retreads of the rejected claim to Hugh as her father.
I was also surprised to see Mary attached to Nicholas given that he's PGM PPP. Over on his profile, "evidence" cited for Mary's inclusion in his list of children includes an odd research note saying "see Stephen Mosher" linked to an odd profile page for a person with a "may never have existed" flag on it, consisting of a mountain of research notes that might be better suited for a free-space page—and on which Mary isn't mentioned at all. The statement on Nicholas' profile that "Evidence showing Nicholas in Rhode Island includes the birth of his daughter Mary in Portsmouth, Rhode Island in 1640/1" is footnoted with a reference to Austin's Genealogical Dictionary of Rhode Island and a link to its page on archive.org that says no such thing! (So there may be problem with the "evidence" for Nicholas' presence in Rhode Island. He isn't in Great Migration Directory.) WikiTreer Dale has posted an astute comment there as well. Responses to his comment include a pointer to another odd research-notes-as-possibly-nonexistent-person profile for Ezekiel Mosher which, again, contains no mention of Mary.
Finally, there are citations to 1990 research by Chamberlain-Clarenbach relating to Nicholas. Only the 1980 edition of their book is available on archive.org and it doesn't mention him at all. The quoted exerpt from 1990 on Mary's and Nicholas' profiles has one tidbit that might be an argument relating to Mary: John Maxson was excused from jury duty in 1677 because his wife and mother-in-law were ill, which must mean, at least, that John's mother-in-law was then living in New England. The authors link this to a 1680 church membership for a Lydia Mosher, claiming that she was the mother-in-law in question. Literally the only thing the church record provides is her name, not even her age. It's asserted that because she was listed directly above Rebecca (Maxson) Mosher, this indicates she was Rebecca's mother-in-law and Hugh's mother. But it tells us nothing about John's mother-in-law or Mary's mother. The same excerpt describes "Hugh’s sister Mary" without any other support. Is there more evidence in Chamberlain-Clarenbach 1990 for Mary that isn't excerpted? Or is that all there is?
Between the five profiles (Mary, Nicholas, "Stephen," "Ezekiel," and Lydia) there are thousands of words and none of those words amounts to any evidence, or even any serious circumstantial argument, for any origin or parentage or surname for Mary. Elsewhere on G2G, there are a lot of circumstantial arguments that you'll see me saying I find possible or plausible, just unproven. This isn't even that.
Anderson has Mary (__) Maxson's origins and parentage as unknown. Anderson even knew about Chamberlain-Clarenbach 1990, because he cites it elsewhere (Hugh Mosher of Casco Bay, GMB 1303-4), which means he didn't think it contained any evidence for Mary. Unless there's something newer that Dale and I are both overlooking, I think Mary should be Unknown, detached, and probably PPP.
Thoughts?