Google only must comply with a non-contested DMCA notice. The moment it is contested, Google is done and has done their job. They are not the copyright arbiters

Google only must comply with a non-contested DMCA notice. The moment it is contested, Google is done and has done their job. They are not the copyright arbiters - that would be the job of the court. By executing a takedown, Google is not acting under the DMCA. They are executing a takedown of an app that may or may not be infringing. They can absolutely be sued or taken to arbitration (ToS withstanding) with no DMCA protection.