The way terminology has evolved over time "Daddy sang bass, momma sang tenor, me and little junior would join right in there..." could mean she was singing the melody, she was singing a harmony in the male tenor range or she was singing the high harmony. Take your pick.
Tenor did start in meaning as melody. According to Grovemusic:
CONTRATENOR ALTUS: "A line in polyphony lying just above the tenor. In the 15th century, as music came to be written in four rather than only three voices, composers approached the addition of the fourth voice by an extension of earlier compositional procedure. The most common arrangement of three voices had been superius (or cantus), tenor and CONTRATENOR; in the new four-voice texture the composer used two contratenor parts, a contratenor bassus and a contratenor altus. In Italy contratenorbassus was abbreviated to bassus, controbasso or basso; contratenor altus became altus, controalto, contr'alto, contralto or alto."