MIT used to have the Billion Prices Project which tried to determine inflation numbers independently of the government, but it no longer exists. My recollection is that it was generally close to the official numbers.

If you think the reported numbers are wrong, you have to give a reason why, backed with evidence. As much as it sucks when rent and food, etc. are more expensive, but those are only part of the number. Inflation encompasses everything and some goods/services are higher than the average number and some are lower. For instance, car insurance has gone up a ton, but apparently fuel oil has gone down (https://econofact.org/inflation-and-prices).

I think what people are (rightly) concerned about is that the necessities of life are higher than the official numbers (because those are an average of lots of things). This makes them think the real numbers are "wrong" based their specific situation rather than the country at large.