Actually, finger-picking goes back to at least the Crusades, when the Christians were influenced by the Arabic cultures (just before they attempted to anniliate it!), and brought back such instruments as the lute, ancestor to the guitar, zither, mandolin, etc.

Also, the ancient Chinese had stringed instruments that they played with their fingers, as well as plectrums.

Modern-day finger-picking goes back to all these origins, not just African.