FWIW, I'm a consultant for a large University hospital, and Dutch. My PhD thesis, years ago, got the remark: "Should have checked with a native speaker." So, now I use ChatGPT to check my English. I just write what I want to write than ask it to make my text more "More concise, business-like and not so American" (yeah the thing is by default as ultra enthusiastic as an American waiter). And 9 out of 10 times it says…
Not by design, but the training corpus necessarily includes a lot of "facts" (claims made by whoever wrote the original text). A model that is trying to output nonfiction on a specific topic, is likely to encounter relatively more models of claims that either actually were incidentally true, or at least have the same general form as true claims without an obvious "tell".
Of course, every now and then it goes off the rails and "hallucinates". Bad luck for the student who doesn't verify the output when this happens (which is probably a lot of students, since part of the motivation to cheat is not knowing the material well enough to do such verification properly).