I don't know about that. After all, when you use the term "fixed timeline", you're only referring to it in terms of time travel. It's fixed in the sense that what is being fixed is the past to those who have meddled with it. And since it is the past, the events have already happened, whether or not they are time travel related. I mean, removing time travel from the equation entirely, the past is still unchangeable, and your choices have no influence over it. It's the present and the future that are able to be influenced by one's choices. That's the point Dumbledore's trying to make. So really, which method of time travel is used really does not have an effect on those themes, at least as far as I can see.