Serious economists mostly suspect that the CPI overstates inflation. See eg
https://www.schroders.com/en/sysglobalassets/digital/insight... or do some Google searches.
In any case, I agree that inflation (or more precisely, the price level) is a finicky statistic to agree on. So if you are making an argument, it's better if you can avoid inflation.
Eg people like to argue whether median real income has stagnated or not. And that crucially hinges on inflation. But what they actually want to talk about seems to be whether workers get 'exploited' more. So we can instead look at the labour share of GDP over time. No inflation adjustment necessary.
The article you linked to is somewhat hilarious. It suggests eg China is cooperating with the US in massaging American inflation numbers. (See point 2 in their list.)
