"…the LLM is being asked to do is to search and summarize new content that isn't in its training data…"

If it fails at that then it is a pretty significant problem. As you say earlier "the refutations are in the training data too", then the LLM should in fact be able to use "both sides" and land with a little better confidence when presented with new data.

(Hopefully your point regarding prompting issues is resolved then.)

Well, yeah, "should be" and "does" are different and this is new technology and has bugs and misfeatures and different limitations than what came before, and the market will have a learning curve as we all adapt.

I was just refuting your contention that this is somehow inherent in the idea of "training", and it's not.