No. Just.... No. The LLM has not "figured out" what's going on. It can't. These things are just good at prediction. The main indicator is in your text: "mostly correct". A computer that knows what to calculate will not be "mostly correct". One false answer proves one hundred percent that it has no clue what it's supposed to do.
What we are seeing with those "studies" is that social study people try to apply the same rules they apply to humans (where "mostly correct" is as good as "always correct") which is bonkers, or behavioral researchers try to prove some behavior they attribute to the AI as if it was a living being, which is also bonkers because the AI will mimic the results in the training data which is human so the data will be biased as fuck and its impossible to determine if the AI did anything by itself at all (which it didn't, because that's not how the software works).