The statement was "AI frenzy almost convinced me that sleep was the training of our neural network with all the prompts of the day."

Prompts are specific to LLMs. Most neural networks don't have prompts.

Additionally, prompts happen during LLM inference, not LLM training. There are many non-technical people who claim they have experience "training" LLMs, when they are just an end user who added a lot of tokens to the context window during inference.