Insurance companies have different rules and guidelines when resolving a claim as do states have differing laws of what an insurance company may do if the insurer of the at-fault party is unable to contact their policyholder regarding a claim. Typically, if the claims adjuster does not contact his insured in a reasonable amount of time they should eventually honor your claim. Some insurance companies though, if state laws allow, will not accept your claim since without speaking to the driver to be able to confirm how the accident occurred and thus accept liability for their policyholder.
You should try to contact the other party's adjuster and discuss your concerns and find out what will happen if the driver does not cooperate with them. You may have to go through your own insurance company first and allow them to subrogate to get their money back. I realize you do not want to use your insurance; however, the alternative is driving with a wrecked vehicle. If you do use your own Collision coverage then your insurer may be able to get back your deductible money through their subrogation with the at-fault party. This claim on its own may not cause your rates to rise, you can discuss if it would with your insurance agent. You may also need to seek legal help for this situation if you want to go after the at-fault party personally.
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