No. If the other boarder did not want to chance her horse being injured she should have not allowed it to be turned out with other horses. If her horse had run through the fence, stepped in a hole then whose fault would it have been?
People need to take responsibility for thier actions or lack of actions and stop blaming everyone else.
It's definitely not your responsibility, nor should you feel obligated to pay her vet bill, but helping her out while he heals would go a long way towards staying on good terms with her. You could offer to walk the horse occasionally for exercise while the wound heals (assuming he's not able to be ridden).
It's not your fault, and you shouldn't pay. I'm quite surprised other border started talking to you about it instead of going to BO. Also since BO was fully aware of situation and that horse has sliders on he/she is responsible for the accident in 1st place.