This is outlandish.
(1) The Federal Reserve has 12 member banks, none of which are private--they're really just branches of the central bank. Those member banks have shareholders consisting of local private banks. These 12 banks don't pick monetary policy. The Federal Reserve board does. Only 1 of the 7 members of the Federal Reserve Board can be picked from the leadership of the 12 member banks. Since the Federal Reserve Board is what actually decides monetary policy, its nonsensical to think of the Federal Reserve as a federation. Because its not. Its a central bank, and has very centralized power.
(2) While banks are part shareholders in the central bank's member banks, IT IS NOT ORGANIZED LIKE AN ACTUAL CORPORATION. They do not 'own' federal reserve banks. They cannot sell their shares, and make no money from them (well, they might earn meager interest). Its literally just a deposit that they make with the Fed that entitles them to send representatives to their regional bank. Even if each member bank was totally dominated by the will of their member banks (which there is no incentive for this to be the case), the sum of their influence on monetary policy is their single representative in the board of governors (who was confirmed by congress!)
(3) The federal government does not borrow directly from the Fed. It issues bonds to the general bond market through weekly auctions directly from the Treasury, and the Fed buys those in the aftermarket to manipulate interest rates. Doing this requires them to add or subtract cash from the money supply. Obama doesn't call Bernake, say "Hey Ben, we need some money for the kitchen we're remodeling", and get the response "Check your bank account, already wired the money! LOL!".
There is plenty of information on the the federal reserve's website describing exactly how its organized.
At the end of the day, if there is ANY chance of the US dollar being replaced by another currency as the dominant currency in the US economy, the central bank will get involved. Moreover, if bitcoin ever gets big enough to have an actual economy that isn't just people converting to US dollar (ie, rent, bills, and wages are paid with bitcoin), we'll have a grand opportunity to test whether having monetary policy is actually a good thing, or if its bad. Because if its bad, and we discover that having a central bank control the money supply is actually a Good Idea, then consumers WILL NOT choose bitcoin.
Hopefully by then there will be some implementation by some central bank somewhere that makes sense, so that we get all the benefits of a digital currency without all the inflexibility of bitcoin's built in monetary policy.