There are a number of reasons for this. The AI could have been trained on misinformation; the answer could require some extrapolation from facts that the LLM isn't capable of; or some aspect of the LLM's training might have incentivized a falsehood

This article seems rather contrived. They present this totally broken idea of how LLMs work (that they are trained from the outset for accuracy on facts) and then proceed to present this research as it is a discovery that LLMs don't work like that.