Come now, that's legal fiction designed to maintain the independence of the Fed. Congress created the Federal Reserve System and could remove it or twist it to whatever shape it sees fit tomorrow if it wants.
There's a good argument to be made that the Fed ran easy-money policies for too long in 2021 in order to secure Chair Powell's reappointment in early 2022; this gives you a clue as to who they are in fact beholden to, despite their nominal independence.
As such, I'm deleting the original text, since I can't delete this comment any more.
My apologies.
You're just saying the same thing with different words. If the Fed or the congress doesn't represent the people it doesn't make any difference to the elite class, who indeed own these two entities.
If this causes worse problems (which it may but hasn't yet) things will simply be changed again.
I'm not familiar with how the Reserve Bank of New Zealand operates, but if it's anything like our federal reserve, the country belongs to the bank, and not the other way around.