In general, if the other driver was to blame, her/his liability insurance will usually pay for a rental car for a reasonable period of time while your car is being repaired but ultimately it depends upon the terms of the at-fault's insurance policy.

In your particular situation it will thus depend upon the terms of the at-fault party's insurance if there is coverage for you to have a rental car, or be reimbursed for one, while your vehicle is in the body shop for repairs. It is normally the insurance adjuster or the claims department that will inform you if you are going to receive a rental car.

Since the at-fault's insurance agent and claims adjuster have given you differing answers I would recommend contacting the claims department of at-fault party's insurance company for a concrete answer if you are entitled, per the terms of the at-fault person's insurance policy, to drive a rental car (and be reimbursed by them) for the time which the car is getting repaired.