Can't be true you need to download songs on each device. When you download a song for offline use you would prefer to have it available on all you devices...
Download songs, albums, and playlists to listen to offline
You can download songs, albums, or playlists to your device so that you can listen to them when you're not connected to the Internet.* You must download songs, albums, or playlists on each device that you want to use for offline listening.
MacBook Pro with Retina display, OS X Yosemite (10.10)