Based on these companies' arguments that copyrighted material is not actually reproduced by these models, and that any seemingly-infringing use is the responsibility of the user of the model rather than those who produced it, anyone could freely generate an infinite number of high-truthiness OpenAI anecdotes, freshly laundered by the inference engine, that couldn't be used against the original authors without OpenAI invalidating their own legal stance with respect to their own models.
Training an LLM with the intent of contravening an NDA is just plain <intent to contravene an NDA>. Everyone would still get sued anyway.