> You don't own media, you just pay for the right to listen/see it. A subtle but important difference

Explain please, in what way do I not own the media I bought?

EDIT: responding to your edit:

> Now of course, technically, Warner can't go after your CD collection

and non-technically, what's the "subtle but important" difference here?

You own the physical media but not the data (song) that’s stored on it. That’s literally what copyright is: the right to copy. You don’t buy that right when you buy the CD.

I kind of expected something that's relevant to the comment the GP made about "owning media" in the context of other distribution mechanism going down (ignoring that I indeed have the right to copy discs I own, for limited purposes), not a "did you know that owning music media means what everyone understands owning music media to mean".

You can’t rebroadcast it for a profit, for example.