Come to think about (if the yellow square hatch on the
Enterprise's teardrop is a docking hatch) the three outer saucers of the space station might allow the docking of a starship from below...
Given the context of the story, however, Kirk wasn't willing to get harbored and audiences might have gotten confused as to where they were (seeing the ship through the station manager's office window provided a clear distinction).
Would have been nice to see such a docking realized in either "The Trouble With Tribbles" or "The Ultimate Computer" TOS-R.
Bob