Read said law. That's not what it requires. The only part of the notice that is under penalty of perjury is "that the complaining party is authorized to act on behalf of the owner of an exclusive right that is allegedly infringed" (H.R. 2281, Title II, Sec. 512 (3) (vi)), not the other 5 required elements of the notice, including the list of allegedly infringing activity.

All of the claims in a DMCA notice are about alleged infringement, because copyright holders are not judges and cannot proclaim infringement to have occurred. The most they can have is a good-faith belief that the use was not authorized, and even if that belief turns out to be true, that doesn't necessarily mean the unauthorized use is infringing. There's nothing wrong with using that language in the notice.