Basically, if you are not near a jukebox when it starts playing a music disk, then go near it, you do not hear it playing.

You can recreate this in multiplayer by having another account place a music disk in a jukebox while you are out of it's noise range, and once the song is playing, move close to it with the account was further away.

In singleplayer, you can place down a jukebox with a hopper above it, power the hopper with redstone, place a music disk in the hopper, then, when you are out of the noise range but within render distance of the jukebox, remotely un-power the hopper. When you re-enter the area around the jukebox, you will hear no sound emitting from it.

While still an issue in singleplayer, I can see this being more of an issue in a multiplayer setting, as it is more likely to happen on accident, instead of you triggering it from afar by yourself.