People love to point out that Saavik was already a Lieutenant at the Academy during her fourth year so it's not the only example. But Kirk's early bio always seems like a hodgepodge and a stew of early ideas tossed into the character's development that don't always make sense.
But then who knows, already being an Ensign at 17 does seem like an overachieving James T. Kirk thing to do.
With admittedly lazy searching on Google, I can't really find anything that points to students as instructors. Maybe Kirk wasn't the actual person in charge of the class, but an assistant that mostly ran the class for the instructor.