The dog threw up in the friends car after pick up. Should I have paid for the car detail and car wash?

Ok, so the dog, lets call him Jim, did FANTASTIC through the stay. Didn't try to eat any other dog's food, got along with others, slept well, did great on walks, etc. Then on a Monday, I only work Mornings, I left the food out for the dogs to come inside to. My boyfriend was taking them on a walk, and I was going to get the food ready. I made sure all the food was separate. However, when I came home, the bowls were together with another dog. I'm not sure if Jim ate the other dogs food or not since my boyfriend messed up. This was around 7am. The dog gets picked up around 8:30PM by the Owner's friend. Jim then throws up in the dogs car. As a sitter, poop/pee/vomit, those are our fuerte. It just takes a little soap, water, vinegar, and maybe even some baking soda. HOWEVER, the owner of course was upset, I told him that he may have or may not have eaten the other dogs food (which I dont think he did, because the other dog had way smaller food than Jim, and the owner said the food was large). I felt awful since Jim was such a bad dog.

Rover doesn't cover the expense, and so the owner expects me to pay it. Personally, I'm not paying for the car wash AND detail for something that is an easy and less than $10 fix. Also, it was over 12 hours since the dog has eaten (Since the dog gets fed once a day). During those 12 hours, Jim was doing great and seemed completely normal. If Jim was to get sick from this food that he may have or may have not eaten, wouldn't he have gotten sick within the 12 hours???? Of course all dogs are different, but the dog wasn't drooling or have any foam, and pooped and peed just fine. It could have even been stress, etc.

So should I have paid for the friends owners detail? It was out of my care, it was over 12 hours from it eating, and it didn't need a detail.