Car Accident: Not my fault, but I swerved missed the car and hit a telephone pole. Who's at fault?

So the oncoming car was turning as I was approaching the car from the other direction. He should have yielded to me but instead tried to turn quickly. I swerved to miss the car and in the process hit a telephone pole. The other driver admitted guilt and stated that in the police statement along with his insurance information. He also stated at the scene that his insurance should pay for it, but I'm wondering whether the insurance companies will see it that way. He has nationwide insurance, I have progressive but I only have liability. What's the story? Who's at fault? Who pays the bill? What are my options if his insurance doesn't cover my damages?|||If the other party didn't actually hit you then his insurer has grounds to deny liability. They can say you over reacted and lost control of your vehicle. Or they may decide to accept liability. The only thing you can do is wait and see.|||I had a similar accident one time, when this stationary telephone pole came up and hit me! Needless to say, the pole had no insurance and I got stuck for it! Shouldn't be allowed!|||The person turning must yield to traffic, so you are not at fault. No worries.|||if the police report puts him at fault then his company will pay.....