The reason handbooks for example say “downloading or transmitting copyrighted material on the company network is strictly prohibited”, is so if a copyright holder attempts to sue the company for an employee’s illegal actions, it can prove it had taken reasonable steps during training to inform employees that the action was strictly prohibited, and their asses are therefore covered.

I’m speculating that the system prompt may serve a similar legal function: even if the LLM did transmit copyrighted song lyrics, we are not liable because as you can see right here in the system prompt we told it not to do that.