Amercan money is printed by the Federal Reserve, which is not a part of the US government, ...
Actually Amercan money is printed by the Bureau of Engraving and Printing, Coinage by the Mint, both under the Department of the Treasury.
The Federal Reserve is a Governmental corporation, much as the Postal Service.
The Board of Governors of the Federal Reserve System is a federal government agency.
The Chainman and Vice Chairman of the Fed need to be nominated by the President and confirmed by the Senate.
The Chairman of Exxon/Mobil does not.