DB Links are one way: one DB (with the link) is the client and the other DB is the server in the relationship, and the server cannot reach back to the client for data or any other information not normally available from any client (basic connection info is made available by the client through the Oracle Client software API).
There is no server-side privilege that specifies whether a client connection may or may not be from a DB Link or any other specific source: any valid database server account can be used as a link target, just like connecting from any other client. There is a client-side privilege CREATE DATABASE LINK that determines whether the link object can be created on the client side.