Humans also make shit up all the time.
Kind of like saying something happens "all the time" and sharing a single example from 15 years ago. Not to mention that a private company's HR team is not the government.
If an LLM makes shit up, your one and only recourse is "computer says no".
I see it every day in the text, images, and video posted by AI proponents on social media. Full of errors and wtfs and the people posting the tripe don't seem to notice it.
Maybe you've just stopped paying attention so you don't notice as much anymore?
Okay. So why should government websites like the French one be well designed? Maybe it should not be.
At the bottom you also have other relevant links (usually to the website of the specific administrations of what you want to do) including reference to the current law that the page is based on (https://legifrance.gouv.fr is also great)
For what I used it for, it was never ambiguous in determining your situation
Honestly, using an LLM the way america.gov does it, is pretty much the same thing as using search engines, except the result you wanted is almost always in the first result, not 2/3 of the way down the 4th page. Or 42nd on a list of things you are not interested in at all. So much more efficient!