You can't change history because it already happened. There are no different paths. Whatever happens, happens in exactly the same way every single time.
As I've said before, Lost is not about changing the past or destiny or whatever--it's about the journey of these people's lives. It's HOW we get to the Incident and HOW we get to the Purge. The events will have always happened that way--it's just in telling how the Losties get where they're going that is the story.
Time is like a record, you can move between songs back and forth, but you can't change the record.
I cannot believe we are still talking about the rules of time travel. lol

I bet you all some cookies that after the finale next year, we'll have people posting, "But why didn't they just let Amy die in the past and change everything?! or something similar.