But if you ask it in terms of a knowledge test ("I'm at the corner of 1st and 2nd, what public park am I standing next to?") a model lacking web search capabilities will confidently hallucinate (unless it's a well-known park).
In fact, my person opinion is that, therein lies the most realistic way to reduce hallucination rates: rather than trying to train models to say "I don't know" (which is not really a trainable thing - models are fundamentally unaware of the limits of their own training data), instead just train them on which kinds of questions warrant a web search and which ones should be answered creatively.