I do this all the time. It's shocking how well it works. A year or two ago suggesting that someone use LLMs for fact checking would get you laughed out of a room, but today the good ones (Fable, GPT-5.6/6) with a search tool enabled are genuinely excellent at this.
They can even retrieve articles you link to and check that you aren't misrepresenting them.
I do something like this with code all the time, “is this idiomatic <foo>?”, I find it very helpful.
This is bad advice for anything serious that can be subtly wrong. I’ve had Fable being consequentially wrong about what a certain, rather small, code block does in our codebase. Not even on something very complex which wasted a lot of time and effort from the team until we checked the code ourselves. I think these tools are still useful and one should learn to use them but blind trust for anything of importance is misguided IMO.