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That being said, how do data havens such as Shadowland, Denver, the Helix, and the rest of the Nexus survive in the political world, without pissing off the wrong folks?
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The documents are still available, and in fact are being mirrored and torrent-seeded at an even larger rate due to the publicity.
Oh look, you answered before you asked

The world is no less hostile to such things currently, yet the information still leaks. It is currently decentralized, though -- SR was around when BBSs were all the rage, and they didn't update to the current P2P trend when they updated the matrix to wireless in SR4. That asside for a moment, look at the net currently -- top level centralized name registrars and country-wide master DNS servers. Many of the current big corps own a chunk of the 'net backbone as well (which has turned out to not be nearly as redundant as people thought.) Add to that the fact that servers, bandwidth, and possibly even storage are somewhat expensive, easily tracked, and easily monitored, and you've got a pretty tight lockdown situation.
And yet... things still leak. The NSA actually issued new digital redaction guidelines in 2005, because a wave of improperly redacted files (with metadata and undo information that revealed "state secrets" -- specifically, state screwups) had hit the web, revealing everything from crappy checkpoint procedures that lead to shootings to "proof" about our pre-ordained plans to invade Iraq. They were freely downloadable from a number of sources, and if any were shut down two more popped up in their place. Such is the nature of the net. Picture that, except that every trashcan, stoplight, and MP3-playing jacket can host the entire hub from anywhere in the world, and the host can change every few minutes. Even with only today's technology, large firewall and shutdown efforts fail. Just look at the "great firewall of China" -- there are no less than a half dozen one-click firefox plugins to circumvent it.
Secondly, with that information I mentioned above freely available, absolutely nothing changed. There was no media riot, no one was arrested or impeached. Essentially, nothing happened because so few went looking, or cared even about the few that appeared in "mainstream" print.
So really, the answer to your question is two-fold. One, in the world of shadowrun -- hell, even in today's world -- squelching information sources on the net is practically impossible and only creates major publicity. Two, there isnt' a real need to shut them down. Sure, the information is out there for anyone who wants to find it bad enough -- but that number of people is so small as to be insignificant to the major players -- especially if the major players have their own media and dirt on any mainstream outlet that picks up the story.
I can just see the Azzi editorials now. "All this talk of waterboard--er, blood sacrifice -- and there isn't any proof that's even happening yet! -- ignores the important issue at hand. We are at war with ____, and if the evil people who attacked us get hurt in order for us to survive, that's the way it has to be!"