ML is my career and I've been doing it for decades. You're wrong. LLMs hallucinate with full context.

Their training data has nothing to do with it unless you’re using a local one without web access.

Did you know that the ones you access online are also trained?

Did you know that any chatbot that can connect to the web was given that capability?

No they hallucinate because they lose context but are tasked to answer anyways.

Nothing to do with context. Context windows are an LLM specific thing, but all neural networks no matter the kind or size "hallucinate" because they are a piece of linear algebra where you put numbers in on one side and get numbers out the other.