No. You are making a mistake. Here are two sentences.
The orange tree is a tall plant that produces sweet fruits. The giraffe is a tall animal that eats sweet fruits.
These are both true statements. But using statistical generation I could easily, from these, generate "The orange tree is a tall animal that eats sweet fruits."
EVERYTHING that comes from an LLM, no matter how it is trained, is hallucinatory. NO EXCEPTIONS. The more often that the statistics match reality, the more likely it is that it will match reality, but even if 100% of the input is factual there is always a path in the stochastic generation that will yield (highly fluent) garbage.
Also, remember that Piltdown Man was written about as a real thing in the scientific journal Nature...