Cubby is built on LogMeIn's own cloud data sync and storage service - not hosted on a third party cloud data platform - and takes advantage of the same online-banking-level encryption capabilities used in LogMeIn's connectivity offerings (like LogMeIn Free and Pro, LogMeIn Rescue and join.me).
After the experiment in the Cambridge cafe, the owners switched to a higher level of encryption for their network, making it impossible to use Firesheep.