AFAIK this really is true. I've seen some videos about patients who had the connecting part between the left and right halves of the brain cut as a (archaic) treatment for epilepsy.

While it did help the epilepsy, their brain was essentially two brains controlling two halves of the body. With one controlling speech. There were experiments where one eye was shown some instruction text, the corresponding hand performed that instruction, and when asked why they dix that action, the speaking half just made up some plausible, yet completely wrong reason, just like an LLM.