The o1 example is interesting. In the CoT summary it acknowledges that the most recent official information is 1611m, but it then chooses to say 1622 because it's more commonly cited. It's like it over-thinks itself into the wrong answer.
How could a language model infer that the official information overrules anything else?
There's limits to how far you can go with this — not only do humans make mistakes with this, but even in the abstract theoretical it can never be perfect: https://en.wikipedia.org/wiki/Münchhausen_trilemma — but it is still the "how".