Well, not exatly. I think right now the RIAA is targeting users who share thousands and thousands of copywritten files. I think if you download you are OK for now. But why would you need to worry about the RIAA, after all, you shouldn't be doing anyting illegal .
However, there are several apps out there that can mask your IP address, encrypt what you download. So if you have one of those programs and do not share, your chances of getting caught are about, umm let me see, you won't get caught.