To start things off, I am firmly on the side of whatever happened, happened. I have no idea why Faraday changed his views from being solidly WHH to thinking he could change a rather large part of everybody's history. Don't leave out the possibility he still believed that whatever happened, happened and only came back because he somehow found that the survivors caused the incident. So this means that he may have come back to insure that the Incident actually happened, and was lying to get Jack and the survivors moving.
This leads to my belief that the survivors didn't change the future. I believe that their actions ensured that the future would happen. I feel that some of the Oceanic Six got sent back to 1977 by the Island to make sure the Incident that brought them to the Island. How ironic would it be, that in trying to change the events that brought them to the Island, they would actually cause the events that brought them to the Island. This isn't too hard to believe. Sayid wanted to kill the younger version of Ben so he wouldn't grow up to be the lying and conniving monster he would become, but we saw that Sayid's attempted murder of Ben did that exact thing- it was the beginning of his path to becoming an Other. I feel this foreshadowed how their attempts to change the future would happen. If Jacob is truly the protector of the Island, and he likes bringing people to the Island, as we can see from the opening scene of Season Five's finale and can infer by his flashbacks with the survivor, then we can definitely see how Jacob and the Island would want to send the survivors back to cause the event that brought them to the Island in the first place. This explanation makes the most sense to me, rather than they were sent back in time to erase everything that happened to them on the Island. It wouldn't be fitting in the Island's way of working so far.
And now specifically about the Incident, and what I believe may have happened. A lot of people are talking about how the survivors may have caused the Incident. This was explicitly referenced to on the show by Miles. I feel that Jughead could have made the Incident so much worse than it could have been, hence why they had to cement over the drilling area and build around it. Sayid's comment about Chernobyl in Season 2 becomes even more important in this context. I also feel that there is possibility that Jughead may have saved the world. In "Live Together, Die Alone" Kelvin Inman told Desmond he was saving the world every time he pushed the button. The button was pushed in order to safely release the electromagnetic energy under the Swan, meaning that every 108 minutes another Incident started, but could be safely stopped by pushing the button. It could be theorized that if it wasn't for Jughead being detonated by Juliet, the Incident would have kept progressing unchecked, and could have ended the world. The nuclear blast, initiated by Juliet, was the same effect as pushing the button. But Radzinsky piercing the pocket of energy made it very unstable, enough so that the energy would have be released every 108 minutes until Desmond turned the failsafe key at the end of Season 2. No matter what Jughead actually did during the Incident, it had always been part of the Incident.