Dog bite neighbours kid?

our neighbours was in our backyard helping fix my car. his 18mth old kid was there playing with my bull mastiff and cattle dog. the bull mastiff got cranky with the cattle dog turned to bite the cattle dog he moved and the mastiff nipped the kid causing a gash about 1cm on her lower cheek. i took the kid to hospital and they put a bandaid on her cheek and said it was alright. no the neigbour wants the dog put down. we have known these people for ten years. are we at fault it was in our backyard