Keynes understood economics quite well, I believe. His prescription for inflation was about politics, not economics. I also believe Bernanke understands it exactly the same way. It is not a difficult concept. That might explain why Bernanke, and Greenspan before him, give contradictory statements. They know a select few will benefit from the inflation, and their job is to make sure that continues.
Greenspan, especially, was noted for complaining about the 'irrational exhuberance' of the market place all the while he was enabling the continuation of that behavior with artificially low interest rates. We know he understood the inflationary factors behind the run up in the market because he wrote a wonderful article in support of the gold standard in the 1960's, and as late as the mid 2000's he acknowledged the article and said he still agreed with every word. Yet he acted in ways contrary to his own stated understanding of how an economy works.
It's not that they are ill-informed, or incompetent, or negligent. It is that they have chosen to take actions that are damaging to the economy for the sake of supporting the ambitions of a select few. They are criminal.