I havent done resarch on the exact wording of Copyright laws, but I /think/ the whole issue is about redistribution without consent. Downloading from someone else isn't you distributing the music, it's them distributing the music. So the problem isn't necesarily downloading, it's the sharing. But the RIAA doesnt want to say "You can download all you want, provided you just dont share" because in order for you to download, somebody else must share.
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"And when I vest my flashing sword And my hand takes hold in judgement I will take vengeance upon mine enemies And I will repay those who hase me O Lord, raise me to Thy right hand And count me amoung Thy saints." - Il Duce, The Boondock Saints