I believe that the Martha Fitts that you are looking for who married Samuel Latham [son of Willliam Latham & Keziah Smitherman] on 23 December 1867 Bibb Co., Al. was the daughter of Walker Fitts and Sarah Needham.
In the 1860 US Bibb Co., Al. Census, Samuel Latham, brother Benjamin and sister Rebecca where listed in the household of their Uncle Rolley Smitherman and Aunt Mary E Fitts Smitherman, and they were not listed as Latham. Rolley did have guardianship of them at that time. Martha Fitts was a younger sister of Mary E Fitts Smitherman.