Thanks guy. I feel great support with your responses, even if I'm wrong I want to get some understanding.
Insurance company wasn't interested in video, but I insisted and send it to them. What I remember can be different from what happened.
I sent the video and then sent another small investigation of mine. Sorry for long message but I want to share with you:
1) If you go step by step through the video and catch each frame you will see that the second car wasn't in the intersection when the traffic light turned yellow. In http://i60.tinypic.com/w9hdfa.jpg the second car's back is visible and I marked it on the pic.
2) Entering an intersection on the yellow light is not allowed as long as you can't stop safely. Anyways she entered the intersection and the light had already turned red (http://i61.tinypic.com/wjgz2a.jpg). As you can see I saw only the front car and waited for it to clear the intersection.
3) Here is another step of the progress. My dash camera is at the front right side of me. It catches the moment but I don't have enough space to notice the car. http://i57.tinypic.com/jv163o.jpg
4) And the red car completely covers the view (http://i61.tinypic.com/261nnk5.jpg). I'm not able to see the car behind. When the light was green (for King street) the only car in the intersection was the one that turned left. And I think there is no other car.
5) And the http://i61.tinypic.com/9blsg8.jpg is the actual surprise.
My green light is starting from the 18th second of the video and we hit each other on 24th second. So she has 6 seconds of red light and she keeps crossing the intersection. As far as I know she can clear the intersection only when it is safe to do so. There could be some pedestrians crossing the street.
I can understand that there is part of my fault too. I need to drive defensively. But now I want to defend my insurance policy rates. And if the video shows I'm wrong, I'll accept that. Anyways you never know what to expect on the road.