Like with everything in law, "intent" is paramount. Obviously it's not the trainer's, nor the end-user's goal to reproduce training set data verbatim; quite contrary, overfitting as such is undesirable.
Intent only goes so far. If I continually but unintentionally reproduce copyrighted works verbatim, I could still face consequences, particularly if I did not show due diligence in preventing it from happening in the first place.