Correct. And since they're not authorized by the copyright owner of the allegedly infringed work the statute should kick in.
For the umpteenth time, no that's not how the DMCA's perjury clause works.
I own the rights to a video I made about dogs. I file a DMCA takedown notice claiming your video about cats violates my copyright.
Because I am asserting you're infringing my video about dogs, and I own the copyright to that video, there is no perjury. I am legitimately filing takedown notices to protect the copyright on the dog video. That your video is about cats is irrelevant to the DMCA. By issuing a takedown notice, I am swearing that I own the rights to (or am authorized by the owner of) the dog video. It is only perjury if I don't own the dog video or am not authorized by the owners of the dog video (e.g. what those lawyers filing lawsuits against people downloading porn were doing - threatening to sue even though they weren't authorized by the real copyright owners, in the hopes that because it was porn people would roll over and settle without a fight).
There's tons of precedent for this, by the way. If I call the police and say "so and so robbed my house today" and then, when they come and investigate and find no evidence that my house was robbed I say "oh, well, not really" - I'm going to jail in that case. That's filing a false report and it's a crime.
Yes that's the way it should work. But that's not the way the DMCA is written. At this point I think the only way this will ever be fixed is if millions of everyday people start filing DMCA takedown notices against stuff owned by studios (e.g. official Justin Bieber videos on YouTube), claiming it violates the copyright on their cat or dog video. Since the DMCA puts the burden of proof entirely upon the accused with no penalty for the accuser, the only way to stop the abuse is to accuse the accusers who are abusing it.