Paul Krugman: do central banks purchases of government debt influence level of interest rates

In his NY Times blog, Nobel prize winning economic Professor Paul Krugman examines the conventional wisdom that the Fed's buying US debt is keeping interest rates artificially low and concludes that this is simply not true.

Given this conclusion is also supported by Fed Chairman Ben Bernanke, your humble blogger is left to ask the question of why then is the Fed engaging in zero interest rate and quantitative easing policies?

If the Fed has no impact on the level of interest rates, these policies are completely ineffective.  So why pursue policies with no benefit?

If the Fed has no impact on the level of interest rates, then why is it trying to claim credit for the pickup in activity in the housing market?