What's under penalty of perjury is the right to file a claim about the work allegedly infringed, rather than the accuracy of the reported content, which merely

What's under penalty of perjury is the right to file a claim about the work allegedly infringed, rather than the accuracy of the reported content, which merely needs to be "a good faith belief". If you publish something you hold copyright on, and someone makes an unauthorised copy, I can't submit a DMCA claim against the copy without your authorisation. Even if the claim would be 100% valid were you to submit it, the courts may enforce that only you and your agents may actually make that submission. On the other hand, it's quite hard to prove that someone is acting in bad faith, rather than being earnest but entirely incompetent.