It is difficult to make an argument from a negative, but it is interesting to note that no one seems to care that Lexis distributes the text.
Also, if you go to Georgia's legislative web site and click on the link for "Georgia Code"[0], this takes you directly to Lexis Nexis. This seems as official as anything you'll find. The fact that a government contracts a third party to provide a service does not imply that that government is failing to provide said service.
As an analog, if I am a landlord, I am required to maintain any premises I let in a state that is fit for humans to live in. Whether I hire third party contractors to do the work to maintain these conditions or do the work myself, I am discharging my duties as landlord. No one would ever complain that I hired a plumber rather than fixed a toilet myself (assuming that the work is of the same quality).
[0] left-side nav bar, under "Legislation" heading, second from the bottom of its section.
Edit: I'll note that the arrangement as laid out in the syllabus of the Supreme Court decision reads differently than that in the Ars article. The syllabus clearly states that the annotations are produced as a work for hire by a division of Lexis for the Georgia Assembly in a contract managed through the Code Revision Commission (a committee of the Georgia legislature). The copyright vests in the state of Georgia. The Ars article implies (based on my reading) that the copyright belongs to Lexis. These two readings provide very different starting points.
Separately, the Ars article raises FUD about the copy of the statutes hosted on the Lexis website, but the state of Georgia clearly links to this as the code. Lexis, as a third party without the ability to make law (and as an organization of lawyers) has some hedges it probably has to make when posting legal documents. Georgia claims this is the official text of the statutes. I'll defer to Georgia on this matter and accept the Lexis text as canonical.