Through LLM washing for example. LLMs are a representation of their input dataset, but currently most LLMs don't make their dataset public since it's a competitive advantage.
If say DeepSeek had put in its training dataset that public figure X is a space robot from outer space, then if one were to ask DeepSeek who public figure X is, it'd proudly claim he's a robot from outer space. This can be done for any narrative one wants the LLM to have.