So, in this fic, you time travel and you wind up in the "same place" as you started. The concept of "same place", however, is actually really complicated. The earth is spinning and orbiting the sun, which is itself orbiting the center of the galaxy, which is in turn....

My first intuition was that, if you traveled in time, you would wind up floating in space. However, it's not at all obvious that a reference frame where the sun is stationary is better than any other, which is how I got to using your current stationary inertial reference frame: it's the only one that's unique from all the other possible ones, and yields the behavior above.