Geithner is probably right in claiming that his handling of the financial crisis compares favorably with that of the 1920s policy elite. (Whether we 'all' have learned from Brüning's mistakes remains questionable. See previous posts.) He is, rightly, proud of that and his choice of interviewer is clearly aimed at emphasizing this achievement: Ahamed's 'Lords of finance' is an impressive collective biography of the central bankers and politicians whose collective failure made the last great financial crisis much worse than necessary. Clearly, Geithner compares favorably to Brüning et al. (Whether we have 'all' learned from history is open to debate. See previous posts.)
However, Ahamed's book ends in 1929. And if we look at the economic recovery after the crisis rather than at the handling of the immediate consequences then it's not as clear anymore that he has learned from history. In the 1930s and 40s economic recovery was made possible by substantial government stimulus. First, it was Roosevelt's New Deal, then military expenditure. It is doubtful that the required volume of government expenditure would have been politically sustainable in the 1930s without the looming military confrontation. But still, government expenditure rose and effectively ended the economic crisis. Geithner acknowledges the need for 'compensating for ... the collapse in private sector demand', but in practice economic stimulus has been far too limited during his tenure. Ahamed rightly picks up on this: growth remains sluggish and unemployment stagnates at his levels in the US.
Geithner has clearly has done his homework about the 1929 crisis. And his plan for the aftermath beats the Monti-Schäuble-et-al plan. But hopefully his successor has a firmer grip of post-1929 economic history.