In going back over this discussion, I see that the two Williams you link are the Elder's father and grandfather, and that I didn't understand exactly whose parents you referred to in your original question. The Mayflower Society does not address the Elder's grandfather at all in the Silver Book which I quoted.
What it does say on page 1 (quoted in my previous comment, above) refers to Elder William's parents, William and Mary (Smythe) (Simkinson) Brewster. The footnote for this refers to his birth date being calculated from an affidavit which was cited in NEHGR [New England Historical and Genealogical Register], 18: 53 (Registry of Affidavits, Letter k, fol.26); MD [Mayflower Descendant], 1:161-163; Dexter [Henry Martyn Dexter and Morton Dexter, "The England and Holland of the Pilgrims, 1821-1890" (Boston, 1905)] 253, 605; MQ [The Mayflower Quarterly (journal), started in 1935], 36: 57.
On page two it says "No birth records have been found for William Brewster or for his wife Mary. Each of their birth years have been determined by calculation from two separate affidavits, which were made by the Brewsters while residents in Holland: (7)
'On 10/12 June 1609, William Brewster made an affidavit, giving his age as "about forty-two." The contents of this instrument pertained to the guardianship of [his reputed niece] "Ann Peck, native of Launde [next Scrooby], when the aldermen of Leiden granted to Thomas Simkinson (8) of Hull, merchant, the power to receive seven pounds sterling that Ann had left in the hancs of william Watkin, pastor of Clarborough [approximately six miles south-east of Scrooby], when she left England.' "
Footnote (7) refers to TAG [The American Genealogist], 41: 1-2 (affidavit #1); NEHGR, 18: 53 (affidavit #2); Dexter, 605.
Footnote (8) Says: "Additional research on the surname of Simkinson may prove and support a relationship to the mother of William Brewster, Mary (Smythe) (Simkinson) Brewster. NEHGR, 124: 250-254 published the present status of research."