IANAL but I've been censored by the DMCA before and fought it. My understanding is that perjury is a crime against the court/government, so you'd have to convince a district attorney to pursue it which is rarely done.
Also, the takedown requires a much weaker statement under perjury than the counter-takedown. "the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly infringed". There's (bizarrely) no need to claim good faith.
