Actually, the marriage certificate is not that important in proving the two men were different individuals.
Many more Primary records prove it.
The 1860 Breckinridge Co KS census shows Bloody Bill's family members, listing him as William T, so who better to know his name than his parents who gave it to him?
ANDERSON WILLIAM C 40 M W KY KS BRECKINRIDGE AGNES TWP 1860
Martha J 36 KS
William T 21 KY
James 17 Iowa
Mary 14 (injured in the building collapse that killed her sister Josephine. Later married John E Thornton and had son John Wesley born 1871, Edward 1873, Frederic 1879, and daughters Minnie born 1874 and Nancy born 1876)
Josephine 11 (died in the building collapse in MO in 1863)
Martha 8 MO
Charles 1 KS
William Columbus Anderson's family in 1860:
ANDERSON WILLIAM 55 M W SC MO STONE PEARCE TWP 1860
Jane 55 SC
James N 21 MO
William 20 MO
Elizabeth Tompson 18 MO
They are living next door to two Byrd families that migrated with them to TX. William's brother David Q preceeded him to TX and married a woman whose sister married one of the Byrds, their family is well documented, start here:
More from a descendant of William C's brother John Henry:
We know William C Anderson claimed he was Bloody Bill, we may not know why, but according to a participant on another Civil War board who is a descendant of William C Anderson's sister, that sister is the one who started the rumor that he was Bloody Bill, when she told the local newspaper. He was therefore interviewed by that newspaper in 1924.
Today's research techniques have proven he was not.