You can take the official inflation values for decades, compute compound growth, and then check old prices to see if the rates were lies.
Hint. They're not. I've done this,and sometimes convince people like you that are convinced rates are lies to do this carefully, and such people then either believe the evidence they checked, or continue believing nonsense supported only by selection bias.
This is the proof. Go do the work, and if you want to claim things are wrong, present the data and calculation.
I didn't read the original comment as saying the data was fraudulent. They were just doubting that "these metrics are a meaningful representation of economic reality", which includes buying a house.
If I'm not mistaken, property prices are not part of the CPI, which makes your comment and the original comment both true. I don't think it's controversial that asset prices have been rising faster than wage growth in general.
I'm no expert on the matter, but sometimes I speculate that the discrepancy between the "data" and the anecdotal experiences is that instead of wages keeping up with inflation, it's more like the core necessities (food, etc.) that comprise the bulk of the inflation index has gotten much cheaper. Which makes buying things outside that group of mass produced stuff feel more expensive.
And then there's also the wage gap between different types of jobs. IIRC lawyers/doctors didn't earn as much more than blue collar jobs in the past. So while in the past a hard working blue collar worker could live a somewhat middle-class life, the pay discrepancy today might not enable them to do so.
As I said, this doesn't mean the official data is wrong, just a matter of how we're "interpreting" them.
Hint. They're not. I've done this,and sometimes convince people like you that are convinced rates are lies to do this carefully, and such people then either believe the evidence they checked, or continue believing nonsense supported only by selection bias.
This is the proof. Go do the work, and if you want to claim things are wrong, present the data and calculation.