I firmly side with the fact that these particular time travelers CAN change the past. (or present).... or future I guess... Just like the Terminator movies. Like Sarah Connor states. "There is no fate but what we make."
However, I think that everyone needs to re-evaluate their own arguments either for or against fate.
First of all, no one should use any type of "what if" scenarios in their theories. EX: "What if Jack went back in time and had sex with his mother? Would he be his own father? Would he cease to exist?" etc. A lot of the arguments on here follow this kind of thinking either for or against destiny. You can't just make some crazy thing up and try to prove it using things that have happened on the show. Theories should be about the show, and the things that have happened on the show. Period.
Secondly, we are viewers outside the experiences taking place on the show. We cannot assume anything to actually have happened one way or another unless it is specifically expressed. EX: Charles Widmore meets with John Locke in Tunisia in the episode "The Life and Death of Jeremy Bentham". Charles has vivid memories about meeting John in the 1950's while he was living on the Island. We have seen Charles Widmore in previous episodes in earlier seasons. Did he remember John Locke then? Did he know about the time travelers from Oceanic 815? Maybe... We don't know. There is nothing that we have seen yet to provide definitive evidence that he has ALWAYS known. Likewise, there is no evidence that the timeline was CHANGED. We didn't see a before and after of that exact moment. Neither could the survivors.
Finally, on to my point. Once something happens it has happened. What could have happened, or what happened in an alternate reality NEVER happened. So there could have been a Dharma Initiative in the 1970's and 1980's that the 815/316 survivors were never a part of, but it wouldn't matter because now it has happened. It's like what Daniel referred to as course correction. An event happens. Period. Charlie died in the Looking Glass Station. Desmond saw other possibilities, and he may have intervened to save Charlie, but Charlie died in the Looking Glass Station. That event happened. Those other possibilities NEVER happened. They MAY have happened if it wasn't for Desmond. They MAY have happened in another reality or timeline. All that matters, all that we know, is that Charlie died in the manner in which he did. Not because it was supposed to happen, but because it did happen.
There was an "incident". That event happened. When it was mentioned in Season 2 it could have referred to ANYTHING. As of the Season 5 finale the vaguely titled "incident" is still yet to be defined. The difference between this situation and Charlie's death is that someone was present who had the ability to see other possibilities. What could have happened. But what COULD have happened is still irrelevant.
Basically, you can change the past. It's just that no one will ever know that you did. Think about Sayid shooting young-Ben and the effect that it would have on older-Ben. A bullet hole scar wouldn't just appear on Ben all of a sudden. No one would be like "Oh shit! Someone just changed the past!" It would be there for his entire life. He would never have known that there could have been a situation where the scar didn't exist.
So it's like the string theory a little bit. Except that I don't personally believe it's one continuous string. I think there are infinite strings moving in every direction. So you may be able to bend the string a little if you're Sayid shooting Ben. Or you may be able to bend the string a lot if you're Desmond saving Charlie's life over and over. In some cases you may be able to bend the string enough that it can overlap or intertwine with other strings; like Jack and the bomb. We have no idea what kind of ramifications will come from this action. No idea. None of us.
The last thing I'll say is that there are hundreds of examples of time travel in literature and visual media. Each of them has very different "rules" for time travel in their universe. Destiny, free will, "course correction", string theory, etc ad infinitum. The creators of this show have left it pretty ambiguous thus far, and really could change all the rules at any moment. And that's pretty awesome!