But there's a lot of cases where there's data about someone that is not owned by them. e.g. If I go into a store and am recorded on the CCTV, the store still owns that video, even if it is about me. This could be pretty similar to the way that if someone uses Facebook and clicks on something, Facebook would own the log which recorded this.
In other cases the data that users upload to websites is definitely owned by them. e.g. If I take a picture on my phone, and then later upload it to Facebook, the photo is still owned by me. However, for any site that allows users to upload photos, it will be part of the terms of service that the users give the site a license to display the photo.