"It is not 'owned' by anyone and is 'not a private, profit-making institution'. Instead, it is an independent entity within the government," however for our purposes this quote is probably more relevant, "the Federal Reserve must work within the framework of the overall objectives of economic and financial policy established by the government."
So, independent, but founded to enact government policy.
While your summary is technically correct, just look at any of your bills. What does it say? "Federal Reserve Note". Your money is not printed by your government. With all the implications that carries, including your government lending it from FED on interest.
"It is not 'owned' by anyone and is 'not a private, profit-making institution'. Instead, it is an independent entity within the government," however for our purposes this quote is probably more relevant, "the Federal Reserve must work within the framework of the overall objectives of economic and financial policy established by the government."
So, independent, but founded to enact government policy.