It's the same "brain", starting from exactly the same prompt, the same context, which means the same thoughts, the same identity... How do you expect it to produce different values?
I guess it depends how you define the LLM: you could say it was the model/NN and the sampler is an extra added on, but a lot of people would name the model+sampler+system prompt+RLHF tuning (which would include the sampler) as the LLM.
The OP was talking about ChatGPT generating fixed output, not an internal model
Also it's an LLM, not a brain.
Instead, exactly as a person would do, it does think of a specific number that feels random in that particular moment.
On the other hand, LLMs show they know very well what a random number is and the fact it just shouldn't look like anything in particular, so they strive to come up with a number that doesn't look like anything in particular. Which happens to be always the same number given the starting conditions.