Filing false report falls under perjury as defined in the statement on the DMCA takedown notice. This would be a criminal matter but as of yet, I don't know of one case where criminal charges have been filed.
In one instance I personally saw, a lawyer sent a false DMCA and they signed it under penalty of perjury for their client. This resulted in a clarification of the perjury that the lawyer may have placed themselves in, and threats to bring it up with the state bar association. Personally I doubted the guy was even accredited in the first place, but the DMCA related harassment stopped promptly.
The only part that is perjury is if you don't actually represent the client you claim to. Assuming the request isn't from a random person pretending to represent a company they don't, the request is not perjury regardless of how frivolous and unwarranted it is.