Earlier quoted context omitted.
The Fed isn't part of the US government. They are a private bank with special powers granted by Congress. When they purchase USG bonds, they hold them and receive interest.
But the Fed pays earnings back to the Treasury. And while the Fed is independent, it's certainly deeply intertwined with the US government. The Fed holding US government debt seems intuitively counterproductive to me.
The Fed is…complicated.
The Federal Reserve Board of Governors is an agency of the executive branch (an “independent” agency, but not independent of the government, independent within the government, like the FCC, FTC, and a number of other boards, commissions, etc.)
The Federal Reserve System consists of a network of Federal Reserve Banks, each of which has a nine member board of directors, six of which are elected by member commercial banks, and three of which are selected by the Board of Governors.
But the actual setting of monetary policy is done by the Federal Reserve Open Market Committee, which has 12 members — the seven members of the Board of Governors, the President of the Federal Reserve Bank of New York, and four of the other Federal Reserve Bank Presidents.