Whether the law is just or current, that is up to debate.
The other labels are contending that Grooveshark employees uploaded the songs and were asked to by management. They claim to have leaked internal documents to prove it.
YouTube didn't upload the content themselves, their users did.
The latter is legal if you comply with DMCA take down, the former is illegal.
This case outlined in the article has nothing to do with either, basically Grooveshark haven't paid a penny to their only major legal avenue to music.
TLDR; Youtube case is nothing like the Grooveshark ones.
Didn't Viacom claim something similar?