- Using a RAG architecture on top of a database of factual information. Wikipedia is probably your best bet. It is not 100% factual or correct either, but maybe as good as it gets. Scaling RAG to wikipedia size is not trivial, but I think it can be done.
- Prompting the LLM to cite its sources so people can fact-check the fact-checker
- Prompting the LLM to say it is unsure when something does not have a clear answer. I don't expect this to be reliable, but maybe somewhat better