Isn't federal reserve a company/bank?
The Federal Reserve system is a mixed private/government system. But its mainly a government system, and the monopolly on money is imposed by the government, who delegates its management on the Federal Reserve.
The only tie the US government has to the private Federal Reserve Bank is that it gets to choose the anointed head of the Federal Reserve whom is chosen from a list of the presidents of those private Federal Reserve Banks.
It would be like saying that McDonalds is a government restaurant if the US president was allowed to choose the CEO from a list of 12 vice-presidents. (and that CEO did not have any special privileges as a majority vote of those 12 VPs would be required to do anything).