Firstly, it doesn't need to perfectly model it. It needs to model it to within a range where claiming to have detected it causes more false positives than acceptable, and given the range of quality of human output that's a pretty wide span.

But secondly, LLMs wired up with a feedback loop and and appropriate IO can model Markov models (models, not chains) which are Turing complete, so a LLM wired up this way is clearly Turing complete as well. As such it's a question of training, not whether or not the model can model it.