So far, I don't think they've encouraged anybody not to use the web. If you used the internet for e-mail for your job or even the web for your job, I doubt they'd say anything. But they've put out strong warnings about the dangers - internet porn, sexual predators, "those posing as fellow Christians (JWs)" with misinformation, etc.
I don't think they come right out and warn you of exactly what they're afraid of. I think they've realized that any publicity is good publicity. So I don't think they come right out and mention apostate websites, but I may be wrong. I think they sort of sidestep it and give you a vague idea about anti JW people out there.
As for calling it satanic outright, I don't think I've seen that. But hey, what do I know? I rarely see their literature anymore, mostly what's posted and quoted here.
But like so many other things, they follow the same pattern. They strongly hint that you shouldn't do it at all, while technically not going so far as to say that. Experienced JWs will get the message and form opinions that the internet is all bad and start looking down on people who use it. Even though the WTBTS did not exactly say that.