The problem here DMCA is that there is a way to prosecute for a false notice, but it's not the one people want it to be.
Most people hear that DMCA notices are sent under penalty of perjury and think that means "if there's no reasonable claim of a copyright violation it's perjury". But the part of the notice that's made under penalty of perjury isn't the claim of violation, it's the assertion that the person sending the notice either holds copyright to the work in question or is authorized to act on behalf of the entity that does.
So to nail someone for perjury from a DMCA notice, you have to prove that they don't hold a copyright, or aren't authorized to act on behalf of whoever does hold a copyright, to the work in question. "This isn't a copyright violation" doesn't do it.
Most people hear that DMCA notices are sent under penalty of perjury and think that means "if there's no reasonable claim of a copyright violation it's perjury". But the part of the notice that's made under penalty of perjury isn't the claim of violation, it's the assertion that the person sending the notice either holds copyright to the work in question or is authorized to act on behalf of the entity that does.
So to nail someone for perjury from a DMCA notice, you have to prove that they don't hold a copyright, or aren't authorized to act on behalf of whoever does hold a copyright, to the work in question. "This isn't a copyright violation" doesn't do it.