She herself hadn't taken the rejection too well, but slaughtering them all would not be the appropriate solution.This was especially a delicate matter, given the fact that the doctor's assumptions had been right all along. The gang's decision to do this, was in retaliation to the indifference of the authorities when no action was taken after the incident at the mine. She sympathised with their emotions as much as she sympathised with Tsuru's, but an eye for an eye did indeed leave the whole world blind.
If they were to take justice into their own hands, who was to stop another band of enraged people from assembling and wrecking havoc yet again, to avenge the Knight's decision. The cycle had to be stopped. The first priority was to save the people and killing a few of their members would probably not stop them from poisoning the water anyways. The head had to be caught and given a trial so that he or she felt that their voice was heard... following which they'd be incarcerated to the fullest extent, for their over reaction or that's what she hoped for.