It is not illegal to download copyrighted material.
It is illegal to upload it.
That is why the RIAA(et al) is looking at users' shared folder(s). They than download the media to prove that a particular user is sharing copyrighted material.
They can't just look at someones' shared media and go on to sue them. What would they sue them for? (until downloading proves the file is as stated)
And, I have yet to hear about anyone being forced to prove ownership of what's on their PC. (software companies not withstanding)