Please explain why it is not incumbent upon the artist to request that someone stop playing a copy of their music in public. Or why - if no digital/physical copies are being distributed - the label should have the right to make such a request.

Also, Grooveshark is in fact operating "legitimately" according to EMI, all of their other partners and legal precedent. Is Universal's approval the arbiter of legitimacy?

It's the fact that streaming digital audio consists of making multiple copies of the same bits that allows them to call it (recording) copyright infringement.

Purchasing music under a personal license doesn't allow one to broadcast or perform the work, so the justification is off.

And it's actually considered the same thing for web streaming — it doesn't have all that much to do with copies. By law webcasting falls under a performance so webcasters are on the hook for both publishing and performance royalties. (Radio gets a waiver on performance royalties and only pays publishing. So the composers get paid, but not necessarily the performers.)

http://en.wikipedia.org/wiki/Internet_radio#US_royalty_contr...

Actually, yes. Bar do get sued when they haven't licensed the music properly, and I recall hearing of instances of them being sued successfully merely for having music played over the radio to a large audience, because it wasn't licensed correctly. Of course, it's only the large labels who actually have the resources to do this; bands would probably generally be okay with it (exposure, increasing the chance of people buying their records or going to their shows).