Or does the conspiracy theory have any finer details I'm not getting or is different?
Was it a conspiracy of the agency to listen in on everyone? Or is the conspiracy that the government ('people in the know') conspired to keep it (a secret agency program) secret?
[0] "PRISM is a code name for a program under which the United States National Security Agency (NSA) collects internet communications from various U.S. internet companies." Wikipedia
[1] "The NSA is responsible for global monitoring, collection, and processing of information and data for foreign and domestic intelligence and counterintelligence purposes, specializing in a discipline known as signals intelligence (SIGINT)." Wikipedia