I'm actually not sure I agree- I think giving a very specific response to your question, even with a 10% chance there is a mistake, along with giving you sources, is pretty helpful: It gives you a good starting hypothesis that you can then validate.

llms tend to make different types of errors than humans, so with this process each can guard against the errors of the other.

Its just more work. If you have to verify from the sources anyhow, why spend effort reading the prompt to begin with? It just wastes your time and maybe even pollutes your subconscious with incorrect information.

That's why the question was whether it gave sources, not whether they asked it to go check sources. Yeah, LLMs suck and you should always assume false information. 80% accurate is not production ready.