Not true at all. It could very well be that when you time travel you go to another version or branch of that space-time brane. Or perhaps the past you visit is purely holographic and read-only in the causal sense.
And if the past you visit is read-only, then you've invented history, not time-travel.
None, because there's an infinite number of branches. And every time someone travels back in time, it creates a new branch.
What'd be interesting is to do an experiment to disprove this: invent a time machine that allows traveling both backwards and forwards in time. Use it to send two people back in time. Person A goes first, and the person B warps back to a time an hour later in the same place, and tells person A a secret. Then person B comes back, then person A comes back an hour later. Have person A repeat the secret, and see if they met each other in the past. With a new universe created every time someone goes back in time, will person B go back to the same new universe that was created when person A went back in time, or will they go back to the original universe that person A tried to go back to, and which still exists without person A which would change the course of history there? Does person B create a new universe? Will person A have met person B, and will they have seen person B go back to the future before them?
It could be the case that time resembles a directed acyclic graph. Traveling "back in time" merely creates a new branch at a point on the graph in the past where that event (the presence of the time traveler) occurs, marking a divergence from the "original" past, in which where there was no time traveler. But you can't ever actually revisit your own timeline, forming a loop.
And, since every quantum interaction would create a new node in which all possible outcomes of that interaction are new branches (many worlds theory,) the concept of an "original" timeline wouldn't even make sense.