"… Nathaniel Barnard, born about 1634, died by 18 November 1659 when his inventory was taken, probably the son of Masakiell and Mary (_____) Barnard and nephew of Mary, wife of Rev. Roger Williams."
Masakiell Barnard appears to have returned, permanently, to England c. 1643 and was living there 1666. Nathaniel would have been nine years old in 1643. Smith's identification of his parents would seem to be possible, but not probable.