You are arguing a minor, irrelevant, and largely incorrect point of semantics.
> Who owns the Federal Reserve?
> The Federal Reserve System is not "owned" by anyone. The Federal Reserve was created in 1913 by the Federal Reserve Act to serve as the nation's central bank. The Board of Governors in Washington, D.C., is an agency of the federal government and reports to and is directly accountable to the Congress.
> Who owns the Federal Reserve?
> The Federal Reserve System is not "owned" by anyone. The Federal Reserve was created in 1913 by the Federal Reserve Act to serve as the nation's central bank. The Board of Governors in Washington, D.C., is an agency of the federal government and reports to and is directly accountable to the Congress.
(emphasis added)
https://www.federalreserve.gov/faqs/about_14986.htm