Peter's book on the Fed represents, among other things, a take on how you figure out what a particular government institution is up to. You could try to do this quantitatively, especially if the part of the Fed you care about sets interest rates. What market conditions predict what the Fed is going to do? You can also do this by going big history, and critical as a matter of policy. That's what Alan Meltzer has done in his two volume history of the Fed, which processes an enormous amount of archival information - minutes, policy papers, etc - to describe what the Fed has done. These days, Meltzer often finds something to criticize. You could also try to understand it purely as a weird culture, which it very much is. Central bankers all talk to one another, only really do central banking throughout the course of their careers, have Ph.D.s in economics, and stay close to the discipline (but not too close! you write a couple of good articles, and then stick to policy with modest empirics.). It's a super insular, almost quintessentially technocratic community. Or you could simply look at its legal authority and examine its rules and orders.
I take Peter to be suggesting that none of these approaches could, if taken alone, provide you with a full picture of how the Fed works. One of the themes that runs through the book is that consideration of the law alone would lead observers to think that members of the Board of Governors are insulated and empowered, when in practice, they cycle through the Fed quickly, and presidents get to appoint many of them. The culture of the Fed, or at least Fed-watching, on the other hand, reifies the Fed chair, and the FOMC, without paying attention to the truly powerful Fed staff, who never leave, even as their leaders revolve away. Finally, Peter rejects the idea that the Fed is a technocratic exercise in the abstruse, but a place where powerful value judgments are made, and so therefore worth some measure of accountability - Matt talks about that. The Fed is much more than a vehicle for monetary policy, as we found out during the financial crisis, and encapsulates a disturbingly large number of bureaucratic actors - Peter is particularly critical of the continued existence of the regional federal reserve banks, and with good reason.
I admit that I prefer these sorts of mixed method accounts, on the assumption that more inputs probably creates a more accurate output. It does complexify things, to be sure. But the Fed is a complex beast, and pretending it is anything but is disengenously reductionist.