The books Supplement to the Nicholas Knapp Genealogy by Alfred Averill Knapp (published in 1956) and Nicholas Knapp Genealogy by Alfred Averill Knapp (published in 1953), lists my William Knapp as the son of Shubel and Rebecca (Mead) Knapp, listing his birth date as 1786.
The information about the "parents," Shubel Knapp (1757-1831) and Rebecca Mead (1767-1830), indicates they married in Fairfield County, Connecticut in 1782, according to the book and in several online family trees. It also appears that Shubel and Rebecca (Mead) Knapp died in Fairfield County, Copnnecticut and did not reside in Dutchess County, New York, although the two counties are neighbors.
Needless to say, there seem to be several problems with the information in the books - If William was born in 1775, then Rebecca would be only 8 years old, and it would be 7 years before her marriage to Shubel Knapp. Shubel and Rebecca (Mead) Knapp did have a son, William Knapp (1786-1830), according to the book.
There are 17 Ancestry Member Trees with my William Knapp (1775-1856), and five of them list Shubel Knapp and Rebecca Mead as his parents. Evidently, they relied on the Nicholas Knapp Genealogy books for their information without looking critically at the dates.
What about other online family trees?
* FamilySearch Family Tree does not list parents for William Knapp (1775-1856).
* Geni.com does not list parents for William Knapp (1775-1856).
* WikiTree.com does not list parents for William Knapp (1775-1856).
* There are two MyHeritage trees with my William Knapp, and neither has parents named.
* There are two RootsWeb WorldConnect trees with my William Knapp, and both name Shubel Knapp and Rebecca Mead as the parents.
I have contributed most of the information about William Knapp to FamilySearch Family Tree, Geni and WikiTree profiles for William Knapp.
I think the answer to my question in the blog post title is NO, William Knapp was not the son of Shubel and Rebecca (Mead) Knapp. I have no clue who his parents were!
It is useful to document these problems in hope that the researchers with William Knapp in their ancestry will see this post and remove the erroneous relationship of William Knapp to Shubael and Rebecca (Mead) Knapp. I could contact the five Ancestry Member Tree owners about this, but have not done that yet.