How easy is this to prove?

[mina_lumina]

We got in an accident yesterday. We were traveling northbound approaching an intersection as the light turned yellow. We went through the light, since it was short notice to stop. At the same time, the woman in the opposing left turn lane assumed we were going to stop and started to turn left. We hit each other's passenger side front. Our insurance company has said, even if we had ran the red light (which we didn't), she would still be at fault for failure to yield, or more plainly, that the person turning left is always at fault. For that reason, we're hoping to use her insurance to fix our car, but they haven't gotten back to us about it yet. My question is, how clear cut is this? We're afraid she might dispute it, though in the end she really is still at fault. It didn't help that the officer didn't ticket her (thus not taking sides on the debate). It was our only car and its not drivable now. I know if she disputes it, it will take longer to get our car fixed and get a rental for the mean time. has this happened to anyone else?