No, CPI includes food, housing and fuel. There is a "core" measure that excludes those, since they add little information but a lot of noise when you want to track the underlying trend.
The difference between core CPI and exponentially smoothed CPI (which removes volatility but includes long term changes in food and fuel) is negligable:
http://www.newyorkfed.org/research/staff_reports/sr236.pdf
There may be gaming in CPI, but excluding volatile components is not it.
Another way to see it: CPI and Core CPI track each other pretty closely, and until recently Core CPI was actually higher than CPI: http://research.stlouisfed.org/fredgraph.png?g=cMs