Actually the operator would likely have called the non-emergency police number, not 911. There was no life-threatening emergency.
That said, better safe than sorry.
No, an operator would not have risked the liability. Phone company employees do not have a hot line to the police station. A telephone operator would have put the lady through to 9-1-1. That's how it works. Phone company employees don't make judgments on emergencies. The lady did the right and speedy thing by calling 9-1-1 herself.
By the way, the last time I dialed "0" it was answered by a women working in a call center in St. Louis. I assume local operators are a thing of the past.