Your friend is correct; a parking lot accident such as yours where you are at-fault and damage another vehicle is what Property Damage Liability insurance is for. This means that the other party makes a claim against your Property Damage Liability (PD) portion of your car insurance policy and there is not a deductible due by you or the other party.

Liability coverages such as Property Damage Liability and Bodily Injury Liability cover those that you may damage or cause harm or injury to without a deductible being due. So if State Farm is your insurer and they accept the person's damage claim they should pay out for the full cost of repairs. If your car had been damaged however and you wanted to make a claim against your Collision coverage than the deductible amount associated with this coverage, $1000 it sounds like, would be due before your insurer would pay for repair costs above this amount.