> If it is never pulling from a source, then why is it able to provide citations?

If you have the training set, and models that summarize text and/or assess similarity, and some basic search engine style tools to reduce or prioritize the problem space, it seems intuitively possible to synthesize probably-credible citations from a draft response without the response being drawn from citations the way a human author would.

Kind of a variant of how plagiarism detection works.