I just purchased an Album from Amazon Music yesterday. It's available with Music Unlimited (which I don't have). I can request any individual song from that album and have it play. I have many songs/albums in that same boat.
Having no other music services does not mean a default music service has been selected in the Alexa app settings. It may well be that "Amazon Music" is selected as the default music library service, but I don't quite get the reluctance to verify that defaults have indeed been set. Where's the harm? I promise I'll shut up about it if one of you would but check.
