If you've got a prompt, along the lines of: given some references, check their validity. It searches against the articles and URLs provided. You return "yes", "no", and let's also add "inconclusive", for each reference. Basic LLMs can do this much instruction following, just like in 99.99% of times they don't get 829 multiplied by 291 wrong when you ask them (nowadays). You'd prompt it to back all claims solely by search/external links showing exact matches and not use its own internal knowledge.

The fake references generated in the ICLR papers were I assume due to people asking a LLM to write parts of the related work section, not verify references. In that prompt it relies a lot on internal knowledge and spends a majority of time thinking about what the relevant subareas are and cutting edge is, probably. I suppose it omits a second-pass check. In the other case, you have the task of verifying references, which is mostly basic instruction following for advanced models that have web access. I think you'd run the risks of data poisoning and model timeout more than hallucinations.