Only short-term interest rates are controlled by the central bank. And that's mostly because the central banks own something like a $$$TRILLION in short-term debt and raw cash, so they simply have enough money to shift the market direction.
In essence: short-term interest rates are still determined by auction, just like any other debt from the US treasury. But when a trillionare is sitting there with ideas about how the market should look like, the trillionare has real power to manipulate the market. Note that these trillions of dollars are money from private banks. Under a "true free market" situation, the Trillionare would still exist! The pile of $TRILLIONS is the money that's been collected by all of the banks in the USA.
In theory, if the central banks ran out of money, they would lose their power to manipulate the markets. But otherwise, the central bank is simply the largest "consumer" on the market. That's the extent of their control. Much like how Apple can buy out the entire 10nm or 7nm production chain for months at a time (preventing Apple's competitors from using TSMC's or GloFo's advanced nodes whenever Apple starts to prepare an iPhone).
Entities with lots of money exert power over the entire market. That's the free market.
Perhaps a better example would be the GDAX Bitcoin exchange. It only will take $25 Million to increase BTC's price to $9000 right now on GDAX: https://www.gdax.com/trade/BTC-USD. It will only take 3000 BTC to drop BTC's price down to $7000, over the short term at least.