Everyone has everyone's data, but the data is encrypted and pseudo-anonymous - meaning you can't get information on someone's transaction without knowing a long bitcoin-address. The latter you can recreate for each transaction for added security. For more information, use a search engine like this one: https://www.google.com/search?q=bitcoin+introduction
What makes the encryption/privacy issue for BItcoin easier is that the data that is stored are just numbers with little or no value on them own: data like 1235.12 is absolutely meaningless when you don't know to whom and what the number applies too But data like a JPEG representing a cat or a text like 'I dated with Alice' already means something on its own.
So our distributed social network would have to store only data of each-other friends. When you use Facebook or similar social networks, it stores data of *everyone*.