Courts have interpreted the statute to mean that perjury applies to a good faith belief in infringement as well. See two cases cited at https://news.ycombinator.com/item?id=23198236
There's no private cause of action for perjury. I agree that it would be nice if some ambitious DA would go after some of the people abusing DMCA or other infringement claims. Or perhaps someone in a state that allows private prosecution?