There's a great story in that Carver biography about Gordon Lish trying to edit Vladimir Nabokov for Esquire in the same way he edited Carver. "Who is this fellow Gordon Lish and what is he doing?" the great man said, according to editor-in-chief Frederick Hills. "We simply return it to him and say, 'This is not possible.'" Nabokov's primary editor, of course, was Nabokov. But most of us can use a real editor, even if it isn't one as aggressive and, ultimately, monomaniacal as Lish.
Whenever an editor (or anyone else, for that matter) asks me to change something, I get my hackles up, just a little. "Who the hell are you to tell me how to make my art?!!?" But the fact is, there are two audiences for your work: the one that contains only you, and the one that contains everyone else on earth. And it's the latter audience an editor is working for.
Dare I say it's the more important audience, as well? The editor, if he's any good, is doing you a favor. He is showing you things about your own work that you're incapable of seeing on your own. He is pointing out your blind spots. A good editor treats the story as something other than a masturbatory enterprise; she is trying to figure out how to make the world accept and enjoy your vision.
There are an infinity of ways to make a story work--and your way might not be among the best, even if you wrote it. Because really, if you're any good, you don't know what the hell you're doing, anyway. Your writing should be a process of discovery, not transcription. When an editor says to you, "We'll publish, but only if you'll do X," consider doing X, and not feeling bad about it. There are times when no is the only possible answer, and I've had times like those. But a lot of the time, the editor knows better--she has seen what you were trying to do and is attempting to help you do it. (I would argue that this was, in the early days, what Lish was doing for Carver.)
Think of it this way: there is no definitive version of anything. Your story is different in the mind of everyone who reads it, because literature is a participatory art, not a dictatorial one. So let up on the reins a little. Your integrity is a strength, but it can turn on a dime into a weakness.