Maybe Kirk thought Pike was hip enough that he'd accept the falsified report and overlook the PD issues given that Kirk saved the people.
well he'd have actually had good reason to think that, considering all the rule-breaking in STXI Pike had overlooked(stowing on board, trying to mutiny, etc.) and had given him a promotion. But because in this movie Pike needs to "teach him a lesson," he reacts differently.
Actually it wasn't Pike that demoted Kirk, Starfleet held some kinf of tribunal Pike wasn't allowed at where they decided to demote Kirk.
Pike just got Marcus to bust Kirk down to first officer instead of all the way back to the academy.