Right you are. I erred. Alfred Newman won the Oscar for scoring the movie. With 26 Berlin songs performed I don't know how there was any time left for a score. I'll learn soon enough. I have it queued up on Netflix.
In that case, Afred Newman won for scoring Irving Berlin’s music. I’m pretty sure that every note in the film was written by him. I guess he won because he was working on the film itself, whereas Irving Berlin just provided the music.