That's kind of letting her off the hook though - yes, it was an accident, but as accidents go it was about as serious a one as could ever happen, and at the very least would have required a stint off duty as a Slayer and probably psychological counseling. I'm a big fan of the character, but brushing what she did aside as collateral damage wouldn't have helped in the slightest.
I'm in no way trying to detract from the taking of a human life, but I still believe that my argument is valid. The Slayer deals with death every time that she goes out on patrol. To simply say that the only minions of evil in the world are either vampires or demons is unrealistic. There are evil humans, humans who have done nothing whatsoever to violate the laws of mankind, so are in no danger from any civil authority, and stopping them should be just as much a part of the Slayer's job as stopping any vampire or demon. Indeed, from what we have seen, neither the Watchers' Council in general, who sent a wet team to capture or kill Faith, nor Giles in particular, who killed totally human Ben without a moment's hesitation, have any hard and fast rules protecting all human life.
The Assistant Mayor's death was a total accident. He had no business being where he was at that particular moment other than carrying out the instructions of Mayor Wilkins (who Giles ran through with a sword, by the way, with every intent of killing him) He was a member of a group involved in a plot to take over the world, as much as any one of Wilkins' vampire soldiers, and, as such, just as valid a target for the Slayer as any one of them was.
Even if we assumed that he was totally innocent of all wrong doing, how would the Assistant Mayor's life be one whit less sacred than Dawn's life was in Season 5, when Giles was quite vocal about sacrificing her if all else failed, or the dozen or so Knights Of Byzantium who Buffy, herself, killed quite efficiently, and with, as far as we ever saw, no regrets? During the centuries since the Shadow Men empowered the First Slayer, do you honestly believe that the need to kill humans has never come up, and been dealt with, before? Do you honestly think that totally innocent bystanders have somehow never gotten in the line of fire before that night? The death of a single human is something that would have to be put in perspective. As heartless as it might seem, the fight can't stop, and the Slayer can't take a stint off duty whenever something like that occurs. Maybe after Season 7, when we have a veritable army of Slayers, such a thing might be possible, but when your entire fighting force consists of one, or even two, girls standing against all of the forces of Evil, both human and supernatural, that simply can't happen.
Giles would certainly known all of that, and should have made certain that Faith was made aware of it, as well. Faith, however, made the fatal mistake of trying to put the blame on Buffy, and that brought out all of Giles' fatherly protective instincts. Faith's great sin, in Giles' opinion, was, I believe, not in trying to hide her feelings of guilt, which would be understandable. What she did, that Giles could not forgive, was her trying to put the blame on Buffy. Giles believed in his Slayer totally. Faith was an outsider.