I just don't think it's a matter of debating whether or not something "exists." Of course anything that is involved in a physical interaction exists. But that doesn't mean everything exists at the same time, and it certainly doesn't mean that the presence of a time traveler in the past requires all events to be predestined. The point is that an event that looks predetermined from the perspective of a time traveler who knows its outcome will not be predetermined from the perspective of someone living through it for the first time. And it's a mistake to try to insist that only one of those perspectives must be the "right" answer. The event does happen, but how it is described and interpreted is relative to the frame of reference. "Predestination" is merely a consequence of observing events from a time-traveling reference frame -- much like how centrifugal force is merely a consequence of observing events from a rotating reference frame. It's valid to talk about it in that frame of reference as if it were a real thing, but if you move to a different frame of reference, then it ceases to be a meaningful factor. To the rotating observer, the pull they feel is caused by centrifugal force, but to the stationary observer outside, that pull is actually caused by centripetal force resisting their momentum. To the time-traveling observer in their relative past, a given event is destined to occur a certain way, while to the conventional observer native to that past, the event is still undecided. The event exists, but how it is described is relative to the observer.
