As I understand it, they claim "under penalty of perjury" only that they own their original work; the claim that the links given actually infringe said work has

As I understand it, they claim "under penalty of perjury" only that they own their original work; the claim that the links given actually infringe said work has no such penalty. My understanding of the logic: It should be relatively easy to tell whether you hold the copyright in a work, unless weird things have happened (see also: SCO). Working out whether a second work is derivative, and if so whether that's fair use? Harder, and the job of a court. That's why it's also really easy to get work re-instated under the DMCA -- at that point, the DMCA has done its bit, failed, and the regular court system takes over.