I've done some more research and it appears to be by design. The music "pinned" is buried and the name of the song not even kept. I guess you can then go through a web browser, download the song to your computer from Google (looks like a limit of twice) and then move it over, but good lord, how cumbersome.
Strikes me as extremely stupid that the default music app with one of the best selling Android devices cannot even access music purchased through google's music store. Very, very strange.