Assuming everyone always stayed in the same job position, this might be true, but advancement within the system is frequently based on whether your work is producing the desired results so when you treat this as a multi round game, their salary level can be tied to the degree which the data they produce conforms to the desired narrative.
One is that a number of governments, including the US, UK, Canada, and Australia, issue bonds linked to inflation. That is, as I understand it, they return a fixed amount over the measured inflation from some index. In other words, understating inflation would reduce the borrower's (the government's) payments.
Another is that Social Security in the US (and maybe similar things elsewhere) is periodically adjusted for inflation, so that the recipients don't lose purchasing power. Again, if inflation were understated, then the government would save money.
There might be other incentives to overstate inflation; the above is just what came to mind, so I am not implying that there is an overall pressure to understate inflation like people tend to claim without evidence. I wouldn't think there are that many inflation linked bonds compared to regular ones.
Ideally the people at or near the top who may have incentives to distort things cannot do it because the low-level bureaucrats keep on doing their jobs. But it hardly seems guaranteed at all times in all places.
But who are those people? The Chairman of the Fed? The Secretary of the Treasury? The President? Let's say the US Government ends up paying $10 BN more on the inflation-linked bonds because of the CPI, how exactly will any of the 3 top-level people listed above going to suffer? Maybe the President does not get re-elected if the deficit is too high? Ha-ha, good joke, after years of trillion dollars deficits, does it look like the voters give a damn?
Ok, maybe I went to high up. Maybe it's people in the second echelon. Or third. Why would any of these guys care how much Uncle Sam pays on the inflation linked bonds, or what the balance sheet of the Social Security Administration looks like? People on the private side often have their compensation linked to the performance of their company (for example by being partially paid in equity), but there is noting similar on the Government side.
So, again, why would any Government employee indulge in any number cooking? What would be their upside?
When organizational failures happen, they don't happen with full transparency or with the participation of everyone in a large organization as if it were one big pyramid. Some people compromise with their conscience, but many others are just trying to balance doing their job as they see it with keeping their manager happy. The dynamics of sub-organizations depend on their directors and how much autonomy they have.
It can certainly happen. But absent some obvious incentives, I prefer to give the benefit of the doubt. (The Libor manipulation was done by people employed by the private sector, who had their career advances and their compensation linked to the way the Libor was marked.) You are right that some non-obvious group dynamics can happen in Government organizations, but based on this generic statement alone, we should refrain to accepting any conspiracy theory without at least a modest amount of intellectual due diligence.
One way is OER, aka Owners Equivalent Rent. Great article https://wolfstreet.com/2021/03/11/house-price-inflation-in-c... (look at that graph half way down).
Another way is "hedonic adjustments". https://www.economicshelp.org/blog/603/inflation/hedonics-an...
Ok, maybe the government has certain incentives, but how exactly do you propose the CPI is manipulated? The guys doing the actual calculation receive a government salary that is fixed, they don't get any bonus linked to the outcome of the measurement. Their bosses don't get a bonus based on how low the CPI comes out either. In fact nobody in the government gives a flying fudge if the deficit goes up or down because the CPI reads this or that. They will receive their salary regardless. Conversely, if one day it turns out they did manipulate the CPI, they may lose their jobs, and even may be dragged in courts for years. All for what? For a government salary? Or are you saying someone is actually bribing them? For someone to bribe them, that someone needs to make a profit. How exactly does that happen?