Big content providers have access to a platform where they can take down videos which infringe their IP by themselves.
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Also they just provide hosting for the videos, they don't upload copywrited content themselves. It's against their T&C to upload a copywrited contet, to which you don't have the coresponding rights.
No, because if that was true, then KimDotCom would have never received the shit storm he did.
Google gets preferential treatment, for obvious reasons.