CPI understates inflation? I’ve never heard that one. It’s quite well known within the economic community that CPI overstates inflation, likely by between 0.5–1.5% per year.
See Francisco Fed article on this: https://www.frbsf.org/economic-research/publications/economic-letter/1997/may/bias-in-the-cpi-roughly-right-or-precisely-wrong/
That’s why the Fed — among many other institutions — uses PCE. I used CPI precisely because it was the more conservative measure.