not necessarily, no. if you have 60% of examples for silence being the hallucination, it just learns the (what you detect as) wrong connection.

Which ... would be overfitting. It picks up on a pattern in the training data that we don't want it to pick up on and which causes it to generalize poorly.

How is it overfitting if the data is garbage in the first place? Saying it's overfitting in this context has no meaning as there is no alternative that maximizes the utility function we're training for?