What the lawsuit focuses on are the ANNOTATIONS. The annotations are short topical summaries that briefly explain what a court said about the statute. An annotation is written by someone who works for a publisher, after reading a court case.
This case may very well hinge upon "who wrote them?". If as you say, written by someone who works for a publisher, that publisher would hold copyright (on those annotations alone!) and would be the party going to court.
But it seems it's the state going to court here. Which means it's the state believing it holds copyright here. Read: state employee(s) writing those annotations. In which case this lawsuit would be a non-starter, regardless of whether those annotations are deemed essential for understanding the law.
Or a (private) 3rd party wrote them for the state, read: "tax dollars at work to produce those annotations". Which imho is effectively the same as a state employee doing the writing.