The connections between what we know as the Internet and what William Gibson referred to as "cyberspace" in Neuromancer can lead to the illusion that his work preempted the World Wide Web. This illusion falls apart in a couple of ways. First, our Internet and Gibson's cyberspace function in completely different ways while still existing for similar purposes. Even through programs/games/interfaces that require us to create an avatar with which to explore and experience things, our online experiences cannot threaten us mortally (barring extreme negligence or carelessness) as they can in Neuromancer; Case experiences brain death three times throughout his forays into cyberspace dealing with the AI Wintermute. Second, the monitoring and regulation of our Internet is completely different than that of cyberspace, at least so far as we see in the text.
As we follow Case and the people with whom he comes to work, we follow clearly illegal online activities, but we do not see much in terms of a criminal justice system to handle these issues. Obviously there is the Turing Squad, but they are rarely ever seen throughout the course of the text and appear to have a very limited focus: the regulation and restriction of artificial intelligences. While they seem capable of addressing or punishing non-AI related cybercrime, we never see them actually do this. Case does not reference the risk of running into Turings unless he's doing something related to Wintermute. In his previous dealings as a console cowboy, the only consequences he notes are those he suffered in Memphis at the hands of his employers. Even when he does finally get picked up by Turing agents, they're swiftly taken out by Wintermute.
Part of the reason this seems so strange is that Gibson does not address how the Turings operate or how they are organized, which couple possibly be symptomatic of the unstable geopolitical state of Gibson's world. As we learn through Armitage/Corto's backstory, there was a war during which most of the technology that Case benefits from was developed, which seems to have greatly diminished superpowers like the United States. While there are still security forces, they appear to lack the authority or powers of an actually police force and struggle to suppress the actions of groups like the Moderns or the crimelords that mangled Case's nervous system in Memphis. This is one of the ways that Gibson's vision works differently than our reality. Our Internet, while largely unregulated and certainly lacking true AIs, appears to be subject to higher surveillance and scrutiny than Gibson's cyberspace. Through legislation like the Digital Millennium Copyright Act and proposed yet failed monitoring like SOPA and CISPA, the United States government has sought to regulate e-commerce and e-communications. The Turings are the only agency we see that has any direct jurisdiction in cyberspace, but it is vague and in the case of Wintermute/Marie-France's plot it is ineffective.
It is possible that this perspective on the role/lack of cyberjustice in Neuromancer is illusory, in that it is heavily skewed by Case's perspective. Practically everything Case does and everyone Case associates with operates outside of any semblance of law. They also shift locations so frequently that it is difficult to say which laws they would actually be subject to, especially in this world that has been reshaped by another war. Case acknowledges that he has killed, but never seems to acknowledge an authority that would punish him aside from the Turings. This is perhaps indicative of the punk side of cyberpunk, the bucking of authority in favor of anarchy. Perhaps we don't hear about these things because Case really doesn't care to even think of them unless they can possibly interfere with his ability to jack in. This, in a way, actually does reflect an aspect of contemporary internet culture. While Congress continues to propose legislation to monitor and regulate the Internet and the social media therein, hackers and pirates continue to manipulate the technology for their own uses and goals.