Greenspan hasn't claimed no fault, to my knowledge, but has claimed that low interest rates did not significantly contribute to the credit bubble. He actually has a decent argument involving correlations between short-term rates, the 10-year treasuries, and overseas savings. However, that is not an argument to absolve the Fed given the regulatory powers that Greenspan squandered in his Fountainhead fantasy.
It just does not make sense to me that Greenspan says "I was not wrong on monetary policy" but "I was wrong on regulation". Who cares? Why confuse the situation? The simple thing for him to say is "I had the power to mitigate this housing/credit bubble, but I didn't". Then he can help answer the question: How can the Fed mitigate the next bubble? Maybe they need to hire a few guys like Michael Burry and fire some of there "best-in-the-world" economists.