Even that is not necessarily true. The output of the LLM is not "Blue". It is something like "probability of 'Blue' is 0.98131". And it may well be 0.98132 for the other question. Certainly they only talk about the internal state in 1 layer of the LLM, they don't need the entire LLM values.
That's exactly what the quoted answer is saying though?
The point I'm trying to make is this: the LLM output is a set of activations. Those are not "hidden" in any way: that is the plain result of running the LLM. Displaying the word "Blue" based on the LLM output is a separate step, one that the inference server performs, completely outside the scope of the LLM.
However, what's unclear to me from the paper is if it's enough to get these activations from the final output layer; or if you actually need some internal activations from a hidden layer deeper in the LLM, one that does require analyzing the internal state of the LLM.