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.
It renders the server that's hosting a leak unable to broadcast the leak temporarily, while they arrange more conventional measures to seize it. It's a more rapid response than getting a warrant and a police team on location. The broad nature of the attack also avoids tipping off the server owners.
I still give it less than a 5% probability, though.
Honestly, that's fairly thin. WL uses torrents and other means of disseminating data that don't rely on central control structures. Plus, presumably, WL has the ability to quickly shift data into secure hands who are willing to release it when things quiet down.
So, sure, the USA could go send someone to sieze the hard drives of someone who has confidential information. But, I have to imagine one of the first steps when getting that kind of information is to disseminate it to others (at least some of whom are unknown to the states). If they were hit, these people would very quickly take that as a signal to indiscriminately release all the information.
Or they could take it down for enough time for other parts of the government and/or international diplomatic system to do their work.
Remember, a data leak is not just a technical issue. They can resolve it in any number of ways - get a small team incursion into another state's territory for extraction, etc. All the outage needs to do is to hold open that window for enough time for all the different parts of the entire threat response chain to do each part's job.
A lot of technical people think tech is the end, but no - if you get a small team to go knock on the person's door, and get your internet response team to shut down dns, or to get someone on site at the telco to perform certain actions at the router/switch level, etc all portions working together is a powerful way to resolve or to accomplish certain goals.
Think bigger, especially with state actors - the resources are there, and this line of thought is probably really basic stuff that people came up with in the 1960's or 70's (even when the arpanet was being created, there was probably already a team tasked with taking such actions - it only make sense to have 2 teams working on such goals in tandem - one to create the network, the other to take it down)
I don't understand how this would change anything unless you're assuming they would take down the Internet permanently