The solution that @DrStrangepork mentioned pointed me to the solution. Basically the problem is iTunes (exists on 12.7.1.14, running macOS 10.13.1). I've yet to find the root cause of this problem (either when a phone call comes in via Handoff or some other problem) underlying cause.
What does work however, is quitting iTunes, playing a video on YouTube via Safari. This kicks/resets the media controls, and re-opening iTunes now correctly binds to the media volume.
Hope this helps someone.