The part which is "accurate under penalty of perjury" is only that "the complaining party is authorized to act on behalf of the owner [...]"; it excludes the part which says "the information in the notification is accurate" from that.
Yes, it means that they can lie as much as they want on the "you are violating my copyright" part as long as they are truthful when saying "this copyright is mine".
Chewbacca is a Wookie, and the claimant is authorised to submit infringement notifications. Neither fact is necessarily relevant to the target of the notification.
- i am authorized by the owner of this piece of copyrighted work
- this copyrighted work appears at this url.
the first needs to be true under penalty of perjury. the second can be as false as you want with no repercussions.
If they're filing a DMCA claim then it indicates that (a part of) the video they're filing a claim against is "this copyrighted work".
But even if you were filing against a video directly, it doesn't mean you're claiming ownership of the video. It could just be one song on the soundtrack, Or a still photo shown without authorization, Or one of the actor's tattoos (seriously) that is the subject of your claim.
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.
Penalty of perjury is criminal. We need a state AG to make an example out of someone. These notices are signed by a natural person, right?
If you really think that a market environment should be able to fix this abuse of the legal system, finding a way through which torrentfreak would automatically profit from this should be a great goal to work towards.
They make excellent bait for precedent cases to to fix a broken system.