James R. Kirk's fist command could have been a shuttle mission at the academy for all we know.
We know very little about how Starfleet appoints it's captains. More than a few nut cases, incompetents, cowards, bigots and idiots have been put in charge of front-line vessels before. Don't think putting a genius third-year cadet who's proven himself capable is the worst they've ever come up with (although it is pretty implausible).
But yeah, believe what you want. It's a mythology, not a right-or-wrong thing. If it really were then the film would have been a remake of some old prequel novel or comic book.
3DMaster: Kirk wasn't wearing a uniform shirt for most of the movie. It's the coloured shirt that has the ranks. When he met Spock he was wearing generic survival gear from the escape pod.