Not an accident that's resulted in an animal being hurt no.
Generally, its not an accident leaving a gate open - its not like ooh no my gate is accidently open. Its a case of I was too stupid to check my gate was shut and I have a big ass dog whose now outside kicking tell bells outa some dog walking past = mis-management.
Accidents do happen and the lady has taken responsibility and im sure will be more careful in future, sure take advantage of her for the vets bills but i wouldnt be reporting her, im sure she has learnt from her mistake and is already very traumatised by what her dog did, imagine if you were in her place.