Bringing up actual communication content is where you start to get onto shaky ground, though, especially considering, for example, the existence of "2 party consent" for recording of communications in some US jurisdictions.

Although I believe that context is entirely for criminal, not civil matters, my point is that there's already a precedent, and a long-standing one predating "data", for the idea that all parties being recorded do, automatically, have a legal ("ownership" may not be the best word, as pointed out upthread) stake in that recording, regardless of which party did the recording or holds the record.

I suspect you used Skype and Verizon, specifically, because, as mere carriers of the communication, they're not really parties to the content that they carry. That doesn't really compare, though, since we're not talking about taping the Spotify songs themselves, and the "ownership" situation there is relatively much clearer, if only because the songs existed previously and aren't being created by the interaction itself.