Your student sounds very like Neville. If we're honest, no one could see why he was a Gryffindor, could they? Until book 5, darling Neville was a Hufflepuff - ie not really suited to any house. Yes he stood up to his friends at the end of PS, and he answered Malfoy back, but it was minor things that didn't really mark him out as particularly Gryffindor - cetainly not in the early days.

I don't think your character needs to understand why she's in Gryffindor. She'll want to understand, but the Hat isn't obliged to explain. Perhaps she argues with the hat, and that's quite reckless of her.