The fact that inflation is going up exactly as much as it should kind of destroys that idea. There are lots of conspiracy theorists that say real inflation is something like 10% per year and the government is suppressing it into a convenient range for the sake of specific policies.

Well, if it were that simple they would simply report another manipulated inflation number and sleep well at night.

Let's assume we accept that there is actually double digit inflation of some sort then what meaning would it have to the economy or monetary policy? Honestly, I'd say it would have zero relevance. Ok, houses went up and now we have to make money scarce and make people unemployed because of that? Building a house creates jobs, selling a house doesn't.