A friend of mine (not on StackEchange) has used LittleSnitch to explicitly disallow Internet access for every process/app that attempted to access the Internet except the ones he actually needs to do this (e.g. Safari, Skype etc.) (to save traffic and maintain better privacy). Everything he wants works great but one thing doesn't - the "Word of the Day" screensaver, it won't show the words, obviously because it can't fetch them from the dictionary server. Looking through the rules list (the blocked executables/apps names) doesn't suggest any obvious candidate to allow. What is the name of the process that is responsible for fetching the words for the screen saver and needs to be allowed?
I believe you should be allowing connections from the ScreenSaverEngine.app, which is located at