And webpages always sound authoritative even when they're wrong.

There’s a key difference to understand: web pages have individual reputation. If I see something about the moon landings on NASA.gov I assign it a different trust level than something I read on youcanthandlethetruth.social, whereas LLM output comes with the imprimatur of the company which made the system. Some LLMs do generate citations but those don’t always exist, come from authoritative sources, or say what they’re listed as saying but users are notoriously prone to not checking unless they’re primed to be suspicious.