This looks less like the LLM is making a claim so much as using an LLM to generate a search query and then read through the results in order to find anything that might relate to the section being searched.
It leans into the things LLMs are pretty good at (summarizing natural language; constructing queries according to a given pattern; checking through text for content that matches semantically instead of literally) and links directly to a source instead of leaning on the thing that LLMs only pretend to be good at (synthesizing answers).