I wondered how Travers would've reacted if he first stopped in to see this new Slayer to see her and Flutie in this scene:
Mr. Flutie: You were there. You saw Dr. Gregory, didn't you?
Buffy: Um, you mean yesterday in the cafeteria when we found him...
Mr. Flutie: Don't say dead! Or decapitated, or decomposing, I'd stay away from D-words altogether. But you witnessed the event, so this way, please.
Buffy: Well, no, I'm gonna be late for biology...
Mr. Flutie: Extremely late! You have to see a counselor. Everyone who saw the body has to see a crisis counselor.
Buffy: But I really don't need...
Mr. Flutie: We all need help with our feelings. Otherwise we bottle them up, and before you know it, powerful laxatives are involved. I really believe if we all reach out to one another we can beat this thing. I'm always here if you need a hug, but not a real hug! Because there's no touching, this school is sensitive to wrong touching.
Buffy: But, I really, really don't...
Mr. Flutie: No, you have to talk to a counselor and start the healing. You have to heal.
Buffy: But Mr. Flutie, I...
Mr. Flutie: Heal!
Travers would probably have a note made to send in Snyder, stat, before their Slayer could be anymore coddled (or worse, saying things she shouldn't...especially seeking counseling over her 18th birthday).
Though seriously, given how disposable Slayers were, I don't see them using counseling, at least beyond indoctrination. Probably a warning and a slap on the wrist for the accidental killing, with advice how to avoid that in the future (*), or at least to cover it up better (and having their own people take care of it, here's a number to call).
(* Though when Travers heard the guy was in an alley of rampaging vampires, I expect he'd find that very suspicious of the man, and even if he was an innocent, he was too stupid to live anyway, especially to touch adrenaline-soaked Slayers rather than waving or whispering to them or even leaving an anonymous note for them to find. And in this case I'd agree with him.)