I am revisiting this discussion because I now believe that John Beal (I need to change his LNAB to Beales) was the son of Edward Beales and Martha Stone (the parents who were disconnected), and I intend to edit the profiles to show this. In view of the strongly worded statements that have been made about John Beal's origins, it seems best to outline the evidence before I implement my plans.
First off, note that I am not suggesting that John Beal was the son of Edmond Beal. Edmond Beal, the father of "John Beal Jr." of Cambridge, was John Beal's brother. Their father was Edward Beales.
The webpage http://beals.info/genealogy/beals/edward_martha.htm treats Edward Beals and his wife Martha Stone; I've not yet seen nearly all the records referred to on that page, but I've successfully used information on that page and other parts of the website as clues to finding sources that confirm key elements of the story told on that page. Another source that I found useful was a letter (link) published in NEHGS Nexus in 1987, from John D. Beal, Jr., of Birmingham, Alabama, who described parish records and other sources he had obtained for this family.
John Beal, who was traditionally said to be from Hingham, Norfolk, is actually documented in Wramplingham and Wymondham, Norfolk, but that's not a consequential issue -- Wymondham is about 6 miles from Hingham and it's about 4 miles from Wymondam to Wramplingham.
Some salient facts: Edward Beales became rector at Wramplingham in 1568 (information confirmed). He married in Wramplingham in 1572 and 1585 (I found record transcripts at FamilySearch or FindMyPast). Those wives died (I've not yet looked for these records), and in 1586 he is said to have obtained a license to marry Martha Stone (I've not seen that record, and there's no parish record of the marriage). They are supposed to have had 14 children; I found the baptisms of sons John (in 1593) and Edmond (in 1595) recorded in Wramplingham (based on record transcripts), with parents of Edward and Martha Beales.
It is generally accepted that John Beales married Frances Ripley. A Frances Ripley was baptized at Wramplingham in 1584 (I found a transcript for this; note: either she was 9 years older than her husband, or the child born in 1584 died and the second one wasn't recorded). The marriage was at Wramplingham in 1616, and I put an image of the register entry on the Beal-9 profile. Baptisms of several of their children were recorded at Wymondham, and Frances Beals was buried at Wymondham in March 1629/30 (that's a record that Torrey apparently didn't find when compiling his 1936-7 TAG article John Beal's First Wife; I put an image of the burial registry entry on Frances' profile and also on John Beal's profile).
Finally, the will of the John Beal Jr of Cambridge, Mass. (which I haven't seen yet, but it's described in sources including the Stone-Gregg Genealogy) mentions his father Edmund and some "cousins." The cousins are identifiable as children of John Beal of Hingham (Mass.), which suggests that the younger John's father (Edmund) was the older John Beal's brother -- and that's consistent with the existence of baptism records for John and Edmond Beales, sons of Edward and Martha.
There are more details, but I hope this is enough to show why I think it makes sense to reject the verdict of this earlier discussion and connect John as the son of Edward and Martha.