In this case there's only one known source. A compilation of Groton records was published in the 1920s, and websites have transcriptions of it. Images are also online, and the date printed was 23rd.
The compilers collated court, church and bible records with the town clerk's records, but they only found the one for Lydia.
The Varnum book was published in 1907, so it didn't get its information from the Groton book. But it probably got it from the same manuscript. Somebody has miscopied it, and without images of the original, we don't know who.
The Varnum book doesn't cite its sources. But presumably they only found the same marriage record that's in the Groton book, with no information about the bride's parents, and jumped to the same conclusion in linking it with the birth. Not that it's at all unreasonable, but it's not evidence.