Second, it's incredibly hard to accurately measure such a nebulous concept as inflation (because there's no such thing as a "general price level"), but it's pretty bold to definitively state that the CPI understates inflation. Measuring inflation is hard. We can buy an iPhone 5 for half what we paid for the first one in 2007--how do we quantify that price change in the CPI? Does a 2013 vehicle that costs the same as its 1995 counterpart represent high or low inflation? It's not just prices that change--quality changes and spending behavior changes. And then we have to take the wildly changing behavior of 300 million consumers, buying god knows how many products, and consolidate that into a single number.
Then that single number has to stand up to those same 300 million people, each of whom is biased by 4 billion years of evolution to be loss averse, to notice bad changes and grow accustomed to good changes, and, inevitably, lots of them will point to things that are much more expensive, unconsciously blind to all the things that have gotten cheaper, and claim that the CPI understates inflation.