American banks don't borrow based on LIBOR. Their overnight borrowing and lending is done at the Federal funds rate [1], an arguably much better-designed system than LIBOR. The only reason LIBOR shows up in the U.S. is people write it into contracts.
> Of the 18 LIBOR member banks, 3 are American
>> Not really reassuring me with those kinds of numbers
The U.S. overruled British regulators in 2008 regarding Lehman Brothers and Barclays, and did so again in reforming LIBOR. The four British banks who are LIBOR members depend more on the U.S. than any American bank depends on London.
> the true ownership (who owns stocks in the Fed) is private
No, the Fed was created by Congress [2]. Its Board is appointed by the President and confirmed by the Senate. It remits its profits to the U.S. Treasury.
Commercial banks own "stock" in the regional reserve banks, but it's more of a reserve accounting mechanism than actual stock. The "stock" is not transferable and confers no management rights; "the Reserve Banks are not operated for profit, and ownership of a certain amount of stock is, by law, a condition of membership in the Federal Reserve System" [2].
> I understand the power of the defense/petro-dollar
The size of the American economy, particularly its consumption, underwrites dollar hegemony. That size means lots of people, within the country and without, must hold U.S. dollars. That, in turn, makes it ideal for lending and borrowing in, which in turn makes it ideal for trading commodities.
> I have repeatedly seen the Fed and major heads of banks bend over for bankers in the City
Since World War II and the implementation of the Bretton-Woods pact the City has served at the pleasure of Washington. For a hint at this, search the British financial press for mentions of American regulators and then do the same of the American financial press for British regulators.