Inflation is worse in a whole lot of countries than the U.S., if you compare the level of inflation in the U.S. to that of most countries, then i think it is relatively low. If i take my country as an example, we are experiencing a very high level of inflation and instability in our economy, but yes, you are correct that the government would definitely not reveal the entire truth in most of the "negative" things they put out.
I don't see how bitcoin fixes this, it is only a legal tender in one country in the world, no mass adoption yet, and you can only spend bitcoin in a "few" places.