The FBC is an official agency. Some people know it exists, but they don’t exactly know what it does, because that’s the whole point of the FBC: errdicare or contain sources of Altered World Events (among other things) and spread misinformation to the public if there were any witnesses. Like they did on Cauldron Lake, by saying it was just volcanic activity.

The FBC has many methods to spread misinformation in order to keep the general public ignorant about the Altered World Events, like the America Overnight radio show. It consists on a series of episodes including people giving their report on some weird experience they had. The show host proceeds to encourage the public to believe it’s about aliens, or ghosts.

Also, there are some documents that explain this situation in Control. Like how the Oldest House (FBC headquarters) is a gigantic office building in the middle of New York that no one seems to be able to notice. It’s not invisible. It’s just that people don’t notice it. It works in a weird way. People that DO see it are people that are SUPOSED to see it. The building itself is a Place Of Power.

About Saga, I think she was intrigued. By the time she understood what the FBC was, interecting with agent Estevez, she was already deep in the weird world that is hidden from us, so I think finding out about an agency that takes care of this kind of shit wasn’t exactly a surprise to her.