I'm probably wrong, but this is how I see it (not sure about the OP).
News cycles happen fairly rapidly, so if you could take down a number of sites that might be friendly to the dissemination of potentially damaging information just long enough such that it's forgotten about, or the attack is so large the media talks about the attack instead, then you might be able to successfully avoid widespread public knowledge of such information. Though, this would be best aided with collusion or cooperation (intentional or otherwise) from the media. Toss in a few unrelated services as a bonus for collateral damage, and you might be able to avoid scrutiny or, at the very least, shift the blame to an unrelated state actor. It won't prevent the release of information, but that's not the point--you want to prevent the dissemination and analysis of that information by the public at large.
This is all hypothetical, of course, and not likely to work. It also comes with the associated risk that if you were discovered or implicated, public outrage might be even worse than if you allowed the release of the information you hoped to distract from in the first place! As such, I can't imagine anyone would be stupid enough to try.
If you take them offline before they've managed to disseminate the info, then it can't be forgotten because nobody knew about it in the first place. Which means when the sites come back on, the info is still newsworthy.
What kind of information would be so sensitive as to risk crashing the economy over, yet so trivial that people would forget about it because they couldn't access Twitter for a day? I get that it's more nuanced than that, but I'm really struggling with this scenario; sensitive information tends to get out if it's important enough, even if you're willing to kill a bunch of people.
News cycles happen fairly rapidly, so if you could take down a number of sites that might be friendly to the dissemination of potentially damaging information just long enough such that it's forgotten about, or the attack is so large the media talks about the attack instead, then you might be able to successfully avoid widespread public knowledge of such information. Though, this would be best aided with collusion or cooperation (intentional or otherwise) from the media. Toss in a few unrelated services as a bonus for collateral damage, and you might be able to avoid scrutiny or, at the very least, shift the blame to an unrelated state actor. It won't prevent the release of information, but that's not the point--you want to prevent the dissemination and analysis of that information by the public at large.
This is all hypothetical, of course, and not likely to work. It also comes with the associated risk that if you were discovered or implicated, public outrage might be even worse than if you allowed the release of the information you hoped to distract from in the first place! As such, I can't imagine anyone would be stupid enough to try.
I'll take my tinfoil hat off now.