It is actually much harder skill. And what worse is that any successful check makes the future checks harder. But there might be no significant improvement on the quality, just the difficulty of detecting the fallacy.

What sort of facts are you thinking of? There are plenty of surface level facts that another model or a human should easily be able to verify as true or not. Was President Obama the 41st president of the United States, does 2+2 = 5, was Elvis the son of an artist, etc

In my sort of informal "How would I like to use this?" testing, this ranges from easily verifiable facts (i.e. "Did you get where I got my degree right?") to structural misunderstandings of important concepts.

The former would be easy enough to fix - though it undermines the utility and if not caught could carry ramifications for people, but the latter genuinely concerns me.