True, but declining interest rates contribute to inflation, no? I think a very good case can be made that substituting Owner's Equiv. Rent for housing prices may be causing the CPI to be significantly understated. Notice the divergence of home prices (go back to the chart) and the CPI once the change was made.
The correction in the CPI was justified. Housing prices reflect inter alia cap rates, and don't reflect the cost of consuming housing. It reflects the cost of an asset. Thus using housing prices distorted the CPI, up and down, as housing prices moved up and down.