State laws and insurance companies rules differ so some may waive a deductible if you are not at fault in an accident but normally the deductible is due if you are placing a claim with your physical damages coverages of either collision or comprehensive. If your daughter was hit by another vehicle then the claim would be under her collision coverage and usually she would have to pay her deductible amount.

Since the cost of the repairs is below your daughter's deductible amount then her insurance company is correct that they would be unable to take her claim and that she would thus need to put the claim through the at fault party's insurance company. Some carriers will handle the claim, have her pay the deductible and then subrograte the claim agains the at fault carrier to get her deductible back. Your daughter's damages should be covered under the at-fault party's property damage liability coverages.

Since your daughter is unable to put a claim through her own insurance company, being that the damage is less than her deductible and thus they will not be subrogating with the at fault party or their insurance company then it is common that an insurance provider will say that your daughter would need to place the claim herself instead of them being involved.

Your daughter's insurance company is not going after the money for the repairs, your daughter is and if she wants a choice of repairs shops, parts, etc then she would need to discuss these issues with the other insurance company herself. If her insurance company had taken her claim and paid out a certain amount for repairs that is when they would become involved with contacting the other person's insurance carrier (or the person themselves) to subrogate or repay the insurance company for the monies they paid out.

If you feel that in your state that deductibles are waived for not at fault claims or if there are other issues your daughter has with her insurance company or more questions about placing the claim she can try contacting your state's insurance regulator.

Normally a state's insurance regulatory agency has a consumer division that will help you with questions of this type or if you want to file a complaint.