You can download an MP3, but you still don't "own" it in the conventional sense. You are licensing it, and a downloaded MP3 is how you utilize that license. If that license was revoked for some reason (admittedly not a likely scenario), continuing to have the MP3 on your system would be a violation.

In practice I doubt this would ever be an issue, but just wanted to point out that you effectively never "own" a digital reproduction of something unless you are the actual copyright holder (or the copyright is permissive), and digital copies can be clawed back in a way that a CD or physical book you purchased cannot.