How many people could he personally have talked to? Probably not 30000 ( his margin of victory). Also, in his case, talking to people might work against him.
I think the name thing is probably a major factor. Both his first and last names might be a clue in South Carolina.
Perhaps some people voted against Rawl because they knew for sure he was white, whereas Greene was an unknown.
But lots of politicians use their name, ethnicity, or ballot position to win. Probably many get someone pay their filing fee. It sounds to me like Mr. Greene won fair and square.
Sergeant Alvin York
But Greene wouldn't have needed to talk to to 30,000 individually to convince them he was black, know what I mean, Vern? All it took was for word to get around. "Hey, he's a brother. Alright."