Yes, it absolutely can.

I'm sure the various high-end intelligence agencies have a much better view on this than the public does. All kinds of ways of cross-checking the numbers, all by doing things they'll be doing in their normal course of events.

A normal person could probably do a decent job with an AI that isn't too biased in the direction of "trust gov numbers above all else" and tracking down and correlating some statistics too obscure and too difficult to fake. (Example: Using statistical population sampling methodology on some popular internet service or something.) The main problem there being literally no matter what they do and how careful they are, they'd never be able to convince anyone of their numbers.