Do you have an image of the 1860 census? [The first link in the OP is from a reliable website and clearly stated "William became one of approximately 184 "free persons of color" in Moore County, NC, according to the 1860 census." The second link, on several occassions, refers to Williams as "African-American" or as a "black man".]
The reason the town kept quiet about his race, and the census recorder (probably at Jones' request) listed him as white, his 1st and 2nd wives were both white. Not a real popular thing during "Jim Crow" in the south! They were prominent people in Carthage, NC. They employed several people. Their business was important to the town. The people had reason to protect them. His white widow received a widow's pension after his death. Her father, a North Carolina Unionist, resigned from the Confederate Army and attempted to take North Carolina out of the war. He ran for Governor (and lost) as a Republican after the war. A very prominent family. Lot's of reasons for the town to protect Mr. Jones. Here's a link to some more detailed info. None of it will say he "passed as white". Honestly, does his photo look white to you? Union P.O.W. records describe his complexion as "ruddy". In the mid-19th century, the biblical definition would have been excepted "reddish-brown". By the way, Jones was listed on every census record and even his death certificate as white. Means nothing when you know the "rest of the story".