It's the difference between data and a physical item. I don't expect to own every physical item I view but I do expect limitless access to my data, especially if I've paid for it.
Even in the case where you buy a song, you don't have limitless rights to it. It would be illegal, for example, to buy a CD and use a song from that CD in a television commercial. You don't own the song, you are purchasing the right to replay the song in some situations. DRM purchases and streaming services are remarkably similar deals.