The problem you are having is not because you are doing something wrong, it's just because the files you are trying to copy are DRM-protected. And that protection doesn't allow you to listen to them on another computer or device. You can do that burning/ripping action, but it takes too much time and is not that "acurate".
Or you can use a software that converts your files into un-protected files to do whatever you want with them(personal use only of course). This is the method I use, very simple and easy to use. The software I use is called
Tunebite. It is the best at the moment, but it costs a few bucks :/.
Tell me if it helped ;)