Dog Bit Another Dog At Groomer - Who's Liable?

To preface the story, this happened to a friend of mine and I was curious who would be liable in a situation like this, as I'm also a dog owner and use a groomer.
TLDR: My friends dog bit another dog while at the groomer and the groomer gave her information to the other dog's vet, expecting her to pay the bill.
My friends dog has never shown signs of aggression - it's hard to say what triggered the fight as the dogs are kept in an open area before grooming and were not closely supervised when this happened.
She got a call the other day from the vet expecting her to pay over $500 for the bill of the other dog. She never told the groomer that her information could be passed on to the other dog's vet.
To me, it feels like she should not be liable as the dogs were under the groomers supervision at the time of the incident and precautions weren't taken to prevent this type of issue - but I have no legal background so curious if this is the case.
Also, is it legal for the groomer to provide one persons information to another client/vet in a case like this?
For reference, this happened in the US in Illinois.
Thanks in advance y'all!
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