I do not understand the claim the Fed is not a government agency?
https://en.wikipedia.org/wiki/Independent_agencies_of_the_Un...
The for-profit ones (Amtrak, USPS, etc.) are called SOEs.
The loan-related ones (Freddie Mae) are called GSEs.
Although an instrument of the U.S. government, the Federal Reserve System considers itself "an independent central bank because its monetary policy decisions do not have to be approved by the president or by anyone else in the executive or legislative branches of government, it does not receive funding appropriated by Congress, and the terms of the members of the board of governors span multiple presidential and congressional terms."[11]