Not entirely true; one of the things that has been frequently criticized about the DMCA notice process is that the only part of the DMCA "takedown" notice that is under penalty of perjury is the statement "that the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly infringed." None of the rest of the material in the notice, notably including the identification of the allegedly infringing material or the statement of "good faith belief that use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law" is under penalty of perjury.
Not entirely true; one of the things that has been frequently criticized about the DMCA notice process is that the only part of the DMCA "takedown" notice that is under penalty of perjury is the statement "that the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly infringed." None of the rest of the material in the notice, notably including the identification of the allegedly infringing material or the statement of "good faith belief that use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law" is under penalty of perjury.
See 17 U.S.C. Sec. 512(c)(3)(A)