By "directly assigned" I mean the case where Grooveshark and a third party rightsholder (record label, artist, etc.) have a deal in place covering the respective track.
70 cents * # of downloads is how lots of artists make money nowadays.
I don't think many people are going to sign a legal agreement and then purposely claim other people's songs. The legal and financial liability from that is huge and much more direct.
Okay, I guess I haven't made myself clear. If Grooveshark costs eight dollars and hour it's going to be out of business in a day. That doesn't help artists. I only see two scenarios, either the 70 cent tax is avoided in which case no artists are helped, or it's paid on almost every song in which case Grooveshark collapses and no artists are helped.