The first and most radical one is Ray Bradbury: A Sound of Thunder (sci-fi short story):

'At this point in the future, time travel has been discovered, and the big fad is to go on safari - Hemingway style: bring 'em back dead - to when the dinosaurs ruled the Earth. The modern world is nice and peaceful, and right now there's an election coming with two candidates for the president's chair. I can't remember their names in the story, but one - John A. - is a democratic guy who isn't planning to make much changes in the pleasant status quo. The other - let's call him George B. - is a dictator type who wants to regulate the whole world and everyone's life. The latter may perhaps get 1% of the votes, but as everybody says: the election isn't much more than a formality; John A. will be our next president. That's why the leading character in the story doesn't mind going to shoot his dinosaur on Election Day.
Now, he can't just shoot any dinosaur. The people responsible for these arrangements know that with so many million years in between, the early death of an animal may have effects on evolution. So before the hunt is arranged, a team travels back in time and identifies an animal that dies a natural death and the hunt is fixed to shortly before its death. They also make paths that the client isn't allowed to leave - can't have him roaming around in the jungle getting in danger.
OK, the mighty Sunday hunter leaves with his guide in the morning. He's led along the pre-made paths, and in due time, a magnificent specimen of tyrannosaurus rex turns up. The man shoots - misses - panics - runs. Not very far, because then this big branch falls from a tree, hits T-rex in the head and kills it. It died a natural death in the original past, remember.
The hunter creeps back and gets what-for from the guide because he left the path. He's only just stepped beside it, though, and nothing has been disturbed, except that there's a little crushed insect under one of his boot heels. Hm, says the guide, such a tiny short-lived critter of which there are millions - no problem.
They go back to their own time - now it's evening - and the badly shaken hunter heads straight for a pub. There's a poster on the wall on which most of the words are misspelled in a very strange way, but he doesn't think much about it. He gets his drink, calms down, and just to make conversation, he asks the bartender: "Well, how was the election?" The bartender stares at him, then he says:
"There was never any doubt about the result, was there? George B. won, of course."'

Too far back to be edited? Hang on for the next story by Elspeth Huxley: The Flame Trees of Thika – Memories of an African Childhood (memoirs, non-fiction).
One episode in the book runs as follows:

'The little girl (Elspeth) is staying with some people and goes exploring in the woods near their farm. She meets an African who's a member of a hunting tribe, and he shows her a place where the buffalos come morning and evening to lick salt. Before she goes home, he asks her if she's got any tobacco. She doesn't, of course, but she wants to give him some next time they meet, so she confides in a young man who works on the farm. The latter gets quite excited about her story because he wants to hunt those buffalos. Okay, there's a hunt, a couple of buffalo are shot, but one is only wounded, and although the young man does what he can to track it, he never finds it.
The girl goes home after a few days, and the next thing she hears is that her hostess is dead. She was pregnant, there were complications during the birth, and the doctor didn't get there in time. It wasn't the doctor's fault, he came as soon as he got the message, but the boy they'd sent to fetch him had to sit in a tree for four hours because he was attacked by a buffalo. He had seen from his tree that it had a half-healed and festered wound on its shoulder.
Elspeth's mother says that the messenger's story is confirmed, so it wasn't his fault, and one can't even blame the buffalo since it was wounded. She blames the young man who wounded it, but the girl defends him; she remembers how he spent all day tracking it.
And then it occurs to her: all this happened because of me! If I hadn't been in the wood, if I hadn't wanted to get tobacco for the African, if I hadn't told the young man about the buffalos, he wouldn't have wounded one. And this disaster wouldn't have happened. Indirectly, it is my fault!'

Easy to edit – just let that buffalo be killed with a good clean shot, right? Remember the first one. If that isn’t enough, here comes the metaphysical angle:

Hans Christian Andersen: The Story of a Mother (fairy tale).

'The mother's little child dies, and she rushes out into the night to catch up with Death and get her child back somehow. She gets help from the Night, a hawthorn, and a lake, and therefore she manages to find the house of Death, but not without great sacrifices since all the helpers want something in return. The house of Death is a garden or a greenhouse filled with flowers, bushes, and trees, some growing beautifully, others not so well. An old woman who works there - and wants the mother's long black hair in return for advice - tells her that to obtain something from Death, she can threaten to pull up some of the flowers. They each represent a human life, and Death is accountable for them to Our Lord.
She tries that threat but relents when Death tells her that she's about to make another mother as unhappy as she. Then he says: "Look into this deep well, and I'll show you the future of two of the flowers". She looks, and she sees one life filled with happiness, love and goodness. In the other life, there's nothing but misery and suffering. Death says: "One of these two flowers is your child, but I won't tell you which one."
The mother screams in terror: "Oh no, save the innocent child, let it go to God, forget all I said!" Then she falls weeping to her knees and prays: "Lord, do not hear me when I ask against Thy will which is the best, do not hear me."
And Death carries her child into the unknown land.'

Until we gain the wisdom of the gods, we'd better not play gods. Or do you think you could administer an edit button?