There is a provision its just not enforced. Whenever someone files a false DMCA claim they are guilty of perjury (which carreis a 5 year jail term).
So when Viacom went after YouTubers who were covered by the fair use provisions, Viacom committed perjury, but nobody pressed charges against Viacom.
If people used MPAA and RIAA content that were strictly under fair use (and lets face it, they do it all the time) somebody needs to charge them, not sue (as they drag it out) but proceed in criminal charges (which legal work is done by the prosecutor) against these organisations. That way you could see Dodd go to jail.