The CPI is a key economic indicator. It’s unlikely that banks and markets would tolerate that kind of meddling.
But, if the CPI was changed for political reasons, there are other similar stats.
In plain language: Wall Street can make or lose billions of dollars based on correctly/incorrectly forecasting this stat, so you can bet your ass they have accurate data. Some of it is private; some is available to paying customers. Even if the data is not public, it is often publicly characterized, for example, in economic forecasts and in publications like The Economist.
Some examples of alternative CPI sources are: PriceStats and The Economist’s Intelligence Unit. Both require paid access.
Be aware that freely-available stats may be published with political agendas, by Fox News conspiracy theorists, etc.