Falsely Accused Dog Bite

I take my 3 year old dog to the dog park about 3x per week and she’s been to formal training (board & train facility) she’s non confrontational, she only plays with certain dogs that she knows, she doesn’t play with toys in the park so there’s no issue of resource guarding. She even moves away from the water fountain when she’s drinking and puts herself in a sit position if another dog comes to drink to give them space and time so she can get back to the fountain and finish drinking. I always have my eyes on my dog, she never goes too far from me as she has a touch of separation issues. Yesterday we went to the park and she was playing with another pup that she knows, when someone walked in with their incredibly hyper dog. The person was on the phone the entire time they were there and our dogs only had a couple interactions, the initial hello sniff and my dog moving out of the way as the hyper puppy zoomed past. There were a handful of dogs at the park so it wasn’t just my dog, their dog and the dog mine is familiar with. I took my dog back to the park today and as I was giving her water, the person with the hyper pup came in the park without a dog and walked over to me and asked if my dog belonged to me. When I said yes, they said “your dog bit my dog yesterday”. I was incredibly confused because if I even got a second thought mint dog got bit or bit another dog I’d check both pups out before leaving the park. I asked to see pictures and I could definitely tell that the dog needed stitches which is horrible. However, it doesn’t negate the fact that my dog is admittedly pretty docile.

So I asked why they didn’t say something yesterday and they told me they checked the wrong side of their dogs body but when they got home they saw the wound. (Remember they were on the phone for the duration of their time at the park). They took the dog to the vet today and tried to demand that I pay for the stitches and medication. They said it’s around $950 but “luckily they have insurance which covers 80%, so hopefully it will not be more than $500”. I gave them my phone number and said I’d follow up although I’m extremely skeptical because I know my dogs temperament.

My dog is white so if the skin was actually broken I’d see the red immediately.

I think none of this is true and I’m being asked to unfairly foot the bill for something we didn’t do. Any thoughts or advice is welcome.