Third Party Claims policy

I logged a Thrid Party claim against my Fully Comprehensive Insurance policy. My insured car was involved in an accident where my car had no damage, but the third party was claiming damages. The Agents came back and said that they would cover the thrid party damages because I was not claiming for damages. I told them that I had no damage so what must I claim for. They were stumped and kept putting me on hold and then coming back and reciting the same thing. I tried to explain to them that the wording they were quoting was indicating that they would handle a claim on my behalf from a third party if I did not do the claim through them and went directly to the third party insurance - by doing this I know that the two insurance companies cannot do their knock-for-knock agreement. The first person I spoke to didn't understand what I was saying and just kept quoting what she understood the policy to be saying, then handed me off to another who did the same thing. Only difference is she said she understood what I was saying but..... I asked them what would happen if I only had third party cover instead of comprehensive and couldn't claim for my own damages if I had any which stumped them