The Federal Bank is only independent from the US Government in a very symbolic way. The system only exists as set out in US Legislation, the President of the US

The Federal Bank is only independent from the US Government in a very symbolic way. The system only exists as set out in US Legislation, the President of the US appoints all the board members and designates which is the chair, they all have to be confirmed by the US Senate, etc. etc. The "private ownership" in that member banks hold stock is also largely symbolic, given that they can't sell the stock and the stock doesn't give them any control, voting rights, etc.