If that's your take-away from that paper, it seems you've arrived at the wrong conclusion. It's not that it's "fake", it's that it doesn't give the full picture, and if you only rely on CoT to catch "undesirable" behavior, you'll miss a lot. There is a lot more nuance than you allude to, from the paper itself:
> These results suggest that CoT monitoring is a promising way of noticing undesired behaviors during training and evaluations, but that it is not sufficient to rule them out.
very few humans are as good as these models at arithmetic. and CoT is not "mostly fake" that's not a correct interpretation of that research. It can be deceptive but so can human justifications of actions.
Humans can learn the symbolic rules and then apply them correctly to any problem, bounded only by time, and modulo lapses of concentration. LLMs fundamentally do not work this way, which is a major shortcoming.
They can convincingly mimic human thought but the illusion falls flat at further inspection.
If you mean symbolic reasoning, well it's pretty obvious that they aren't doing it since they fail basic arithmetic.