Watters: Sir, I'm Captain Watters. Captain Ramirez gave me a battlefield commission.
Admiral: Captain my ass... get those pips off this minute, cadet. And don't you go near the Valiant unless it's to collect your belongings. Expect to be on the next shuttle back to Earth and the Academy!
And yet, this episode gives us the precedent that allowed Trek'09 to happen. After saving the day, Kirk should have been granted a commission as a Lt jg, and told to report to the Lexington. Effectively only skipping the Ensign rank, and only because he saved Earth.
As far as Valiant, I always thought it was jacked up that Collins accepts a brevet as a Chief Petty Officer... something that as a cadet she'd already outrank. Even Nog is confused when trying to figure out what rank she holds.