Orin is right, as is commenter Huh?, and I'm wrong. I let myself get suckered by the plaintiff's complaint in DiMemo v. Max, which asserts that the anonymous annoying speech ban is enforceable in civil lawsuits by private parties.
In fact, as Orin points out, the ban is an amendment to a criminal statute (47 U.S.C. § 223), and can only be enforced by the government. D'oh! I just glossed over this issue, because some other recent telecommunications legislation (e.g., the junk fax statute, 47 U.S.C. § 227) provides a private right of action, and I assumed that plaintiff's lawyer wouldn't just make up a civil claim where none exists. Silly me, and damn you, Matthew B. Weisberg, Esq., Attorney for Plaintiff.
In any case, thanks to Orin and Huh? for the corrections; my concern about the criminal statute stands, but this of course makes this incident a much less direct example of the statute's mischief.