Question: Does a DMCA takedown mean the material taken down was infringing?
Answer: No. ISPs can take down material according to the DMCA anytime they receive a compliant notice alleging copyright infringement (see What are the notice and takedown procedures for we...?). The ISP does not have to investigate to determine whether the material was truly infringing before taking it down. The fact that someone has claimed infringement does not prove that infringement occurred -- there might be a fair use defense, or the claim might have been false or even frivolous.
In order to ensure that copyright owners do not wrongly insist on the removal of materials that actually do not infringe their copyrights, the safe harbor provisions of the DMCA require service providers to notify the subscribers if their materials have been removed and to provide them with an opportunity to send a written notice to the service provider stating that the material has been wrongly removed. [512(g)] If a subscriber provides a proper "counter-notice" claiming that the material does not infringe copyrights, the service provider must then promptly notify the claiming party of the individual's objection. [512(g)(2)] If the copyright owner does not bring a lawsuit in district court within 14 days, the service provider is then required to restore the material to its location on its network. [512(g)(2)(C)]
A proper counter-notice must contain the following information:
The subscriber's name, address, phone number and physical or electronic signature [512(g)(3)(A)]
Identification of the material and its location before removal [512(g)(3)(B)]
A statement under penalty of perjury that the material was removed by mistake or misidentification [512(g)(3)(C)]
Subscriber consent to local federal court jurisdiction, or if overseas, to an appropriate judicial body. [512(g)(3)(D)]
If it is determined that the copyright holder misrepresented its claim regarding the infringing material, the copyright holder then becomes liable to the OSP for any damages that resulted from the improper removal of the material. [512(f)]