NeverBeenSeen It is industry practice to only take down with DMCA because there is no way to verify who the copyright owner is. By issuing a DMCA, you are legally binding yourself and if you are lying, it's perjury.
In a DMCA request, there is a statement they have to say that the information is accurate to their knowledge under penalty of perjury.
And you say that the company is bringing legal trouble to itself, the first cause of action IS the DMCA.