Right, insurance follows the vehicle and by using a valet service you're obviously giving permission for them to drive your vehicle. If the valet company insurance won't agree to cover the full cost of repairs, then the owner can go through their own insurance who will then subrogate against the valet company after the fact.
I had a case like this in New York a few weeks ago, valet parker hit my insured's vintage Porsche in a long term parking garage. I called the valet company, they said they would take care of it, and haven't heard back from my insured since. Usually in cases like this the valet company would rather pay out a few hundred bucks and settle the damage vs. drawing it out over months and months. Even more so in long term residential garages like that.