My name is XXXXX XXXXX I'd be happy to answer your questions today. I'm sorry to hear that this happened.
Insurance companies decide whether to pay claims based on a variety of factors, many of which are based on probabilities, charts and graphs rather than who is legally responsible. Insurance companies will usually say that a person who hits the rear of another vehicle is responsible. However, that determination is not binding on a judge in a civil case.
A person who is injured in a car accident (or has property damage) has a right to sue the other driver for the damage that was caused. The judge has to determine whether, more likely than not, you rear-ended the other driver, or whether he cut you off while making an illegal turn. If the damage is on the side on the car, rather than the back, that supports your version of events. If you had a witness in the car, that would help but is not required. This is not a criminal case, so you don't need proof beyond a reasonable doubt. Just keep in mind that your damages are capped at the Kelly Blue Book
value of the car, even if it could be repaired. A police report would also help, if police were called.
Hopefully, your pictures and explanation will be enough for the insurance company to see that this was not your fault. If it isn't, then you would have the option of suing the other driver. The suit is against the driver, not his insurance company, but if he's covered by his policy, they will pay the claim following a judgment. If your insurance company pays the claim, and you sue the other driver, you have to repay the insurance company from the proceeds of the suit. It's also important to look at all documents you receive or sign. If your insurance company pays you the value of the car, that often means that you have to assign them your right to recover against the other driver (so they can sue him to get the money back if they want).
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