Indeed, you are not alone!
And no need to feel foolish. The protective cover looks like a menu option, complete with battery icon, and even lights up when connected to your computer. Your post helped me figure out that it was a cover, and needed to be peeled off. I was ready to send this back to Amazon!
Mags1230 is right, it should be made of clear plastic, or instructions given in the users manual telling you to remove it prior to plugging in your Clip+ for the first time.