Every child whether legitimate or not is the descendant of the mother’s parents and a descendant of the father’s parents and Samuel Longbottom, Sr., may have had grandsons named Bottoms who did not carry his male DNA, but they were still his biological grandchildren if they were born of one of his unmarried daughters.
The documentation for the Longbottom descendants of this Pitman line is based primarily upon: the 19 Jan 1805 will of Sarah Longbottoms which identified some of her brothers and sisters, the children of Samuel Longbottom, Sr., and Cela Pitman, daughter of Benjamin Pitman; and, other children surnamed Bottoms who were born in the time frame in which Samuel Longbottom, Sr., was documented as married to Mary Pitman, daughter of Benjamin Pitman (before 23 Aug 1755 and after 24 Aug 1769).
There is no known individual born before Aug 1813 with the surname Bottoms who was definitely not a descendant of Samuel Longbottom, Sr., and who was not a descendant of Benjamin Pitman through his daughter Mary or his daughter Cela/Celia, except for a child or two children of the widow Alaminta Bottoms who was in Nash Co NC Court in Aug 1813 concerning her illegitimate child and again in court in Aug 1816 concerning her illegitimate child named William Bottoms (and no records for that William Bottoms or for the widow Alaminta Bottoms have been found after Aug 1816). A widow such as the widow Alaminta Bottoms could have had a child with the Bottoms surname who was not a descendant of Samuel Longbottom, Sr., and his father-in-law Benjamin Pitman, but any illegitimate child of a daughter of Samuel Longbottom, Sr., would still have been a descendant of Samuel Longbottom, Sr., and his father-in-law Benjamin Pitman.
The widow Alaminta Bottoms became a widow in 1795 and there appears to have been no opportunity before 1795 for an illegitimate Bottoms who was not a descendant of Samuel Longbottom, Sr., and his father-in-law Benjamin Pitman as the widow Alaminta Bottoms appears to have been the first Bottoms widow in Edgecombe Co NC or Nash Co NC.
A Bottoms widow could have given birth to a Bottoms non-descendant but a daughter of a Bottoms descendant could not have given birth to a Bottoms non-descendant.
William Longbottom (Sr) of Surry Co VA died between 20 Feb 1733 and 18 Jul 1733, leaving a will. His widow Jane Jones Longbottom remarried to Francis Hutchins before 18 Apr 1735 and, as all the children of Jane and William Longbottom (Sr) were recorded in the will and in later estate records, we know the only people surnamed Longbottom in VA were their sons, born 1725-1733, possibly born 1721-1733:
There was no known Longbottom in North Carolina at that time and the only Longbottoms recorded in Edgecombe Co NC before 1779 were Samuel Longbottom, Sr., and his wife Mary Bottom (sic), married 1752-1755. There were neither sisters nor sisters-in-law of Samuel Longbottom, Sr., who could have been the mother of William L. Bottoms, born in or before 1755, or Beulah (Buly Bottoms) Baker, born about 1761. The oldest possible child of Samuel and Mary Longbottom could only have been born after 1752 and would have been only 9 years old in 1761, so Beulah (Buly Bottoms) Baker could not have been a grandchild of Samuel and Mary Longbottom.
Again, there were no single Longbottom women or known Longbottom widows in Edgecombe Co NC who could have been the mother of William L. Bottoms, born in or before 1755, or Beulah (Buly Bottoms) Baker, born about 1761. Given that Lucy L. Bottoms gave birth to Temperance Bottoms in 1788, probably at least 18 or 19 in 1788, born in or before 1771, it almost impossible for her to have been the daughter of anyone but Samuel Longbottom, Sr., and Mary Pitman Bottom (Mary’s only recorded surname), as the only other possible Bottoms parent, William L. Bottoms, was only 16-18 years old in 1771.