Using Find a Grave for reference, I discovered that Sam's parents were Nathaniel Henry Hyder (1847-1935) and Mary Isabell Williams Hyder (1851-1921). Nathaniel's parents were Samuel Washington Hyder (1817-1897) and Lavicia Elizabeth Edens Hyder (1824-1870). Samuel's parents were Michael Hyder II (1767-1861) and Sarah Eisenberg Zimmerman Hyder (1780-1865), from whom our line of the family is also descended. Michael's father was also named Michael and fought in the War for Independence. His parents, Hans Michael Hyder and Katherine Chasteen Hyder sailed from Germany to America by way of Rotterdam and Philadelphia in 1729. This makes Sam my second cousin three times removed.
Incidentally, Milligan University is a Christian university in the Restorationist (Stone-Campbell) tradition of the Christian Churches, Disciples of Christ, and the Churches of Christ. Sam's great-uncle Jacob Hyder (1814-1881), my third great-grandfather, was a trustee of the Union Church of Christ, located in nearby Washington County, in 1876. That two members of the extended Hyder family were associated with the Churches of Christ suggests that others might have been as well, but I've not found concrete evidence of this.