I bet that in her previous modern life, she had a copy of the completed song or had played it before in music class or something. That or she might have come across the artist behind the song and was performing it in secret in the past.
I'm not sure I'm willing to agree to the "body's memories" theory in this case. For a lot of reasons, it doesn't sit right to me. But, oh well, I'll accept it for now. Wondering if we'll have another explication in the next chap.