While doing some research about yet another set of Great Migration immigrants, I came across the following that I thought might be of interest.
Source: Donald Lines Jacobus, "Culver and Winthrop" in The American Genealogist, 22 (1945):108:
Ten years later, a Culver pedigree was included in the Registration of Pedigrees... published in the New York Gen. and Biog. Record (51:90-92). Here the unequivocal statement is made that John2 Culver married, previous to 1665, Mary Winthrop... "That she was daughter of John Winthrop is established by the bible records of the Culver family of Groton... [my emphasis] photographic copies of which are filed with the New York Genealogical and Biographical Society." ...
The danger of accepting statements in Bible records without thorough investigation of their authenticity has often been demonstrated, and even photographic copies are not always conclusive, since they afford no opportunity for the study of the paper and ink, but merely for the style of script in which entries were written. The date of publication of the Bible in question is not mentioned, so we lack even that criterion as to how early the entries could have been made.
In general, entries in old Bibles which were made contemporaneously with [at the time of] the events, or not too long after, may be accepted as reasonably correct. However, serious misstatements are sometimes encountered in Bible entries, due to various causes... those who entered their family records a century or more ago sometimes include traditional or legendary matter...
(and it goes on to discuss even forged bible entries sold fraudulently)
So keep this in mind when you encounter a claim that "it must be true because it was recorded in the family Bible."