As much as records compiled in a collection by the government involved can be reliable and definitive, the parentage claim for William V. Adkins as being John Adkins & Elizabeth Bromsall (often cited as Bromwell) in Bedfordshire has been disproven. The William born to them on 28 Mar 1689, appears to have died an orphan around age 15, still in that location, on 9 Sep 1704. He never reached adulthood or left England.
PDF of images extracted from the 1933 compilation (drawn from the original parish registers’ long-hand writing) are available, as is the original full compilation on archive.org (“Bedfordshire Parish Registers VI, Sandy, Little Barford”, published under the auspices of the County Records Committee of the Bedfordshire County Council, and of the Ven, the Archdeacon of Bedford, 1933, edited by F.G. Emmison, Clerk of Records, Bedfordshire).
I created a PDF of the extracted relevant record images, available on request to couchdouglas@aol.com (Doug Couch, descendant of William V. Adkins).