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It's a good attitude to have (not having the tendency toward litigation) but it might really hurt you here. Insurance companies are the people you will be up against and I can tell you from being in small rear-enders (where I was hit and the other was 100% at fault) that the ins. people are absolute bastards and you will want to strangle them once you start dealing with them. Remember, you are going after the insurance company and not the people. They will shut you out of medical care and physical therapy as soon as they are able and, most likely, way before you are healed.
I don't want my rates to go up as more and more suits are filed, but yours is totally justifiable.