Yes, that is true, but it is still part of their mandate. Supply and demand of money gets reflected in inflation and the Fed responds by changing interest rates. Isn't this a free market mechanism?
No. In Friedman's "Monetary History of the United States" he shows how the Fed setting interest rates was rather erratic and much more unstable than the earlier free market mechanism. The Fed would guess at what the S+D point was, since the Fed was not subject to market forces. This meant they were always late and always wrong.