The BLS CPI has major flaws, as noted in Shadow Government Statistics' deconstruction of the chained methodology. SGS's annual inflation estimate is about 4-7% higher than the official CPI, depending on the base year. Most mainstream analysts aren't interested in checking this discrepancy.
So-called worry about a "downward wage-price spiral" seems to me like a straw man. Fed economists probably know about the government's flawed reporting. The Fed members most worried about deflationary price moves are the members of Bernanke's pro-inflation faction who want to continue the bond-buying program. Concern about igniting inflation is actually driving more reticence inside the Fed, according to FOMC meeting minutes in April. It's important to note that the purpose of indefinite QE, as Fed members have admitted, is more about supporting asset markets that will generate a hoped-for "wealth effect" on consumer spending.