Earlier quoted context omitted.
They'd need to immediately shut down their server as well (as in immediately , as in crash), and even that's not necessarily enough to remove data from RAM before attackers can get to it.
The threat scenario is a bit far fetched. First you'd need to find out where an individual, interesting piece of data is stored. Then you have to break into this building, break open the cabinet and freeze the RAM fast enough to preserve the memory content. That's obviously something that can be done, but it requires a lot of dedication to pull of, so that's something you'd only do in case where you know the data is…
The very first people to sign up will all be budding security enthusiasts secretly looking forward to their prime time on Chaos Computer Club or BlackHat or whatever where they take apart one of these servers.