Increased the size of the popup. Now it shows the whole button caption:
Confirming what I said, this is the front module permission, which is used only to "store" some methods but the player itself is added via hook in the profile controller, that's why the permissions won't work specifically for this case.
To control who can upload or not musics, go to ACP -> Members -> Groups and enable it for the groups you want. It doesn't appear for guests but currently guests can play musics in other's profiles. There is no restriction for this.
Fixed:
Just took a look and there's no way to do that via player, like when you click to change the buttons color. It would have to be a setting on ACP or something like that.