By analogy to humans: if this model were raised in a cult, and then let out into the real world, it would be seemingly incapable of unlearning the cult’s indoctrination, despite the real-world data all contradicting it — as all of this real-world data would be too surprising for the model to accept.
Or, for a maybe-more-likely situation you might encounter in e.g. incremental model re-training of old models for chronologically-newer info: a model trained this way would “stubbornly” refuse to accept any major shift in scientific consensus on a topic.
The human cognitive architecture seems to solve this problem by 1. buffering this rejected-for-being-too-out-there info in a way where it can at least be pattern-recognized; and then 2. noticing when a lot of different, seemingly independent, seemingly trustworthy sources begin matching on the rejected pattern. At that point, the human brain seems to swing the other way — experiencing a “crisis of faith” per se.