Earlier quoted context omitted.
What is the distinction between a "line office" and HQ?
HQ is a building with highly paid bureaucrats sitting in Washington, DC or its suburbs. A line office would be say a branch of US Immigration and Customs that you deal with at your local airport.
Line offices are at the pointy end of the stick where you actually deal with citizens. In my particular case we do a lot of permit issuance and resource management, but yeah think local branch office where you go when you want something.