Agree. But Fed rate fixing is not lock step. Banks go the Fed window for "Very" short term money. The Fed does not originate deposits themselves. Long term money is provided by investors. There was a time when many Texas banks self financed from the oil industry. I remember what was done in the collapse of the Republic Bank (on the charter called: The Republic of Texas). NE Money centers were like vultures, they hated how Texas banks operated. Too free.
Federal Reserve discount rates are a leading factor but do not actually control interest rates charged by specific banks. Now, as far as nations are concerned, I'm less sure how the mechanics work. I've not heard much lately about the Export/Import Bank and their policies. Think I heard they were very active in Central and South American activities. There were large problems with corruption in that bank during Obama.
The rates that the FOMC sets for practical purposes do have a direct effect on the money supply, short term yields, short term interest rates and the strength of the dollar. Raised high enough they have caused recessions, crashed the stock market, and triggered global financial problems.
So yes, the Federal Reserve does manipulate the markets, something Conservatives should be against.