Probably the same reason that the Federal Reserve Bank is not a government entity (they only have a meaningless government "oversight board") even though it loans all money to the US Government with interest and has never been audited.
- was created by the US government
- is ran by US government appointees, who are nominated by the President and confirmed by the Senate
- has to make annual reports to Congress
- returns all its profits to the US government
- describes itself as a government agency. [0]
Does the Fed have more independence than, say, the Department of Agriculture? Yes, but an independent government agency is still a government entity.
[0] "The Federal Reserve, like many other central banks, is an independent government agency..." https://www.federalreserve.gov/faqs/about_12799.htm