The model just asked the crawler to get a recent copy of relevant pages and used that to give the answer. That is why AI companies experimenting with browsers or at least agentic extensions to browsers as that allows to fetch on behalf of the user directly from the device with a residential IP and ditch expensive to maintain crawling infrastructure.
Index is just a part of the model. The nice property is that the index for LLM does not need to be updated often so LLM plus index can be static. This even works for the latest news as LLM can fetch major news sites to learn the latest stories and then fetch individual articles for the final answer.