As an Rdio shareholder I was told that the labels did have equity, but certainly not a majority stake. I'm not sure exactly how much they had.
... as well as plug https://spotbot.qa/, which he is working on with another early Rdio employee.
It seemed strange to me as well (esp after seeing how much outside funding they had raised), but the people I heard it from seemed both credible and adamant. It's also possible that the cap table has changed since I heard this (years ago) and now.