These models have so many parameters that, while insufficient to memorize all text it has ever seen, it can end up memorizing some of the content. It is the difference between being able to recall a random passage versus recalling the exact thing you need. Both allow you to spill content verbatim, but one is problematic while the other can be helpful.

There are techniques to allow it it 'read on demand', but they are not part of the core model (i.e. the autocmpletion model / LLM) and are tacked on top of it. For example, you can tie it search engine, which Microsoft's copilot does, and is something which I don't think is enabled for ChatGPT by default. Or allow it to query a external data bank (Retrieval Augmented Generation).

Do you read a song on demand when you are singing the lyrics verbatim?

It's definitely not indexed, we use RAG architectures to add indexing to data stores that we want the model to have direct access to, the relevant information is injected directly in the context (prompt). This can somewhat be equated to short term memory

The rest of the information is approximated in the weights of the neural network which gives the model general knowledge and intuition..akin to long term memory

Steelmanning what this person said, I think the issue is that your ability to CTRL+F through a book during a time-limited exam is not as strong as even a single computer clocked at GHz doing the same thing. You can CTRL+F through a single book in the same time it takes it to CTRL+F through the entire body of knowledge.