This is straight from the vault(fallout wiki)
Come 2077, with total nuclear war rapidly arriving at America's doorstep, the President of the United States and a number of other United States government officials left their posts to take refuge in a number of secret locations around the world. Among them was the Poseidon oil rig. Here, the President himself set up a secret base from which the USA could continue to exist and wage war on China, with the eventual goal of retaking the continental United States.
The oil rig was there hq
The goverment and The Enclave are two different things.
Brotherhood of Steel: Now I will admit i love the Brotherhood( hence my name) but the brotherhood needs to change, or it is going to go the way of the Enclave. The NCR is Kicking the Brotherhood's ass in the west, and depending on the Courier's actions, the Mojave Chapter might prosper or fail( i try to help them prosper unless i am playing House or Legion, even then i wait for the last moment to blow them up) In the East, Lyon's Brotherhood of Steel has the right idea, and I think their idea should be spread to the rest of the chapters out west, or else they will die out for being so old fashion with their ideals, Hell, the last Maxson agrees with Lyon's ideas, and he is a kid! Casdin and his Outcasts need to quit crying over spilt plasma and just get over it, Lyons got the better tech and equipment, and got the location of the Super Mutants to stop them, so rejoin Lyon's Brotherhood and stop whining that your not on your original mission. As for the other Chapters in the United States, we will have to see, or wait to see if they will be confirmed as Canon.
There are already other people out there helping people, like the Followers of the Apocalypse (and the NCR to some extent), but The Brotherhood has a Codex to follow. If you don't like it, you are free to leave.
It's like asking the Red Cross to join the fighting in Afganistan, really.