You earn the badge by winning the battle. This badge was essentially a "Thanks for being a good kid and saving the Pokémon" badge. Calamity already brought up the fact that Pikachu didn't want to battle so there's no point in brining it up since it wouldn't play a factor.
Also, Ash sucked back then if you didn't notice. He was a new trainer just like Misty so it's not as though he was leagues better. Take into consideration that she knew more about battling and Pokémon it's doubtful one could make the case that he was that much better than her especially in a Water-type gym without Pikachu.