I have not verified this, but here's the story I've seen:
In 1873 David killed his next door neighbor, Thomas Archibald. The accounts can be found in the Ouachita Telegraph Saturday September 13, 1873 page 3 column 1. The story is that David and 2 other men murdered Mr Archibald at the gate in front of his house with shotguns to the chest. It was believed that Mr Archibold was to be a witness against them for theft of Hourses and /or cows. After the killing the other 2 men were caught and killed, while David fled to Texas and changed his name to William Talton Phillips.
I have traced the Phillips line down to myself. Going backwards, I found David's father, Miles (1818-1860), as you referenced, and his father, John Floyd. Here is the 1850 United States Federal Census about John Floyd:
Name: John Floyd Age: 64 Estimated Birth Year: abt 1786 Birth Place: Virginia Gender: Male Home in 1850(City,County,State): Western District, Franklin, Louisiana Household Members: Name/Age Amanda Floyd 32 David S Floyd 1 Elizabeth Floyd 3 John Floyd 64 Martha J Floyd 16 Miles Floyd 32 Adline Iler 12 Clinton Iler 14 John P Iler 8 Robert H Iler 4 Malissa Iler 11