They really don't. You can run the numbers yourself. All the prices that it's computed from are public, the methodology is public and it's dead easy to backtest. Dead. Easy. (1 + (Inflation / 100)) ^ (Years). Inflation would be the dumbest possible thing to lie about because it's so damn easy to check.
The conversation always goes like this.
You: "The government is lying about inflation!"
Me: "Ok, what rate do you think it's actually been?"
You: "10%!"
Me: "So you're telling me inflation over the last 30 years was 1700%? So prices are now 17X higher than in 1995? You sure?"
Then we look up historical prices like this.
https://www.tasteofhome.com/collection/this-is-what-grocerie...
In 1995 ground beef was $1.49/lb.
Bread was $.89/loaf.
Eggs were $0.92/doz.
Milk was $2.50/gal.
idk if you're shopping at Erewhon but where I shop ground beef isn't $25/lb, bread isn't $15/loaf, eggs, well, you got me there lol, and milk isn't $42.50/gal.
Unless the conspiracy is far bigger than we think, or "they" are everywhere, whoever "they" are, I think it's safe to assume that inflation numbers have been pretty accurate.