There are a number of GEDCOMS on the internet purporting to show that Henry's and Richard's parents were a Daniel Bristol b. ca 1595 in England and Hester Sperry also from England.
Henry did have a son Daniel, by his 2nd wife Lydia Brown, which Daniel md. a woman named Esther Sperry. It is extremely rare to find both a son and his wife named exactly as the son's grandparents, for one thing. But the problem is more complex than that.
To my knowledge there was only one Daniell Bristow born in England and chr. 24 Aug 1595, but at Crosthwaite, Cumberland. The purported records have their Daniel almost anywhere else.
Next, Henry was b. about 1624 and the only Daniel Bristow/oe's who were married about that time were (a.) to Margaret Raithbecke, 20 Jan 1617, Horncastle, Lincoln and the other (b.) to Mary Armstronge, 1 May 1623, All Saints, Newcastle Tyne, Northumberland. The problem is that there is so far no recorded progeny of either marriage. So we're hard put to make either of these the parents of Henry and Richard.
Furthermore, Henry and Richard spelled the name Bristow, not Bristol. All the purported LDS records have the spurious parents' name spelled systematically "Bristol." Also, none of these "reports" (not records) have any specific parish location for Daniel, or Henry, or Richard, which means that the reports were not derived from parish records, but from someone's imagination.
The LDS does a good thing when it copies records. It does a bad thing when it allows unsupported theories to have the same status as proven records.
For 32 years I have been involved in Bristol genealogy and history. I have yet to find one legitimate researcher who has ever come up with this theory. The Bristol Family Association has no such theory. I've never seen it anywhere except on GEDCOMS citing each other and IGI files, which I have just described as spurious.
Genealogy is both a game of discovery and a serious pursuit of knowledge. The game is great fun. But it's time to get serious before we publish unsupported theories. I have one ancestor whose linkage is only supported by an enormous amount of circumstantial evidence which is almost unshakeable, yet I continue to search for that single item which will prove my hypothesis once and for all.
Another thing you will also find in these spurious GEDCOMS is the switching of Lydia Brown to wife #1 and Rebecca ____ to wife #2.
They will often also leave out the name of Rebecca altogether. I have known several descendants of Henry and Rebecca ____ over the years, one a Judge, and I don't think he , or they, would approve being demoted from elderhood in the lineage.
Finally, as a descendant of Henry and Lydia Bristol of New Haven, I am extremely uneasy about people ascribing ancestors to me that I cannot find any, even circumstantial, evidence for.
I put this message here to implore you to remove this erroneous material from your GEDCOMS before you publish them on the internet. If you are professional about what you are doing you will do this.