There exist several US federal bureaus, such as the census and labor statistics ones, that have built and maintained widespread trust in publishing accurate tabulations. It is not an impossible problem.
Uh... There are plenty of people who seem to think census results are rigged in one way or another. E.g. I think I've seen that the infamous Heritage Foundation (I know, I know) has some beef with The Census bureau over some under-counting or something like that.
If anything, I'd love to see more zero-trust approaches to government, where possible (voting, statistics, etc). No idea if that's going to work, but probably worth a try.