Fot those of us who don't generate enough revenue for Google, the offender is here
https://archive.org/stream/visitationshrop01grazgoog#page/n186/
Camden's name is on the 1623 Visitation, but he never did his own, he sent deputies. They didn't take blank sheets, they took copies of the 1584 Visitation, to update them by adding the latest generation.
John Withie was an arms painter who traveled with one of the deputy heralds. He made his own copy of the report and added stuff from his own collection. Presumably his additions can't easily be distinguished.
This manuscript got around a bit, with pedigrees added in other hands, before it ended up in the Harleys' collection.
This is the basic source of the book. (The title pages are rarely accurate descriptions of the content.) Notes in Roman type and square brackets are additions by the editors.
The 1584 Visitation was done by Lee as deputy for Cooke. Office copies exist, but George Marshall, a herald, said they didn't look like a proper visitation. One Jacob Chaloner obtained a copy, and of course made additions to it. Later one Hanford (suspected of not being the most accurate copyist) made a copy of Chaloner's, and Hanford's copy ended up at the British Museum. This is the source for the bit in italics.
Lower down the pedigree there are bits in italics and round brackets. They come from a different manuscript, said to be copied directly from the original of the 1569 Visitation by Cooke. From this we learn that part of the pedigree, at least, existed in 1569 and was copied forward into the later Visitations, with the usual sprinkling of accidents in the process. This is why there are no books of the earlier Visitations of Shropshire - the material was copied forward into the later ones.
(Elsewhere in the book, additions in italics and square brackets come from a 4th manuscript.)
So basically the offending parents can be pinned on Jacob Chaloner. But we're left wondering how all these long pedigrees were put together in the first place. They're typical constructions of pedigree-mongers and I suspect Cooke and Lee did more in the office than in the field.
PS fixed link