If I remember correctly, to properly install or remove a cover, you actually have to unbolt the changer from its mounting to slip part of the cover through/around the mounting bracket, and then it sits in place. I can definitely see mechanics in a hurry short-cutting this process and not re-installing the cover because they forgot this. I've done it myself a few times, and it's a minor PITA to unbolt the changer to get the cover around it properly.
My two cents.
Cheers,
Gerry