The exact chain of command can be supplanted if a particular duty officer is made the officer of the deck (like Geordi in TNG season one) where a senior officer might be expected to follow the orders of a junior officer. It's part of officer training.
I would question the wisdom of leaving 17 year old NuChekov in charge of the bridge though when there must have been a decent number of more experienced officers to summon from elsewhere on the ship.
But it is annoying that Uhura did not get to sit in the chair in any of the later movies either. They did it once on a Phase II (fan series) episode where Uhura gets out of the chair as Kirk returns to the bridge. It was simple, brief, and cool!