You could say the decision to go to war is also ultimately under democratic control. Yes, it is, but it doesn't necessarily mean you should trust a politician or president when they want war.

Similarly, you shouldn't necessarily trust a central bank when they want to print money. (I'm not inherently opposed to it and think the pros probably outweigh the cons for some situations and intents; just saying accountability in cases like these isn't as simple as "it's the people's will".)