if you might have watched the series carefully, you wouldn't need to argue. In some recent episode, when pa sage was training naruto, he explained that to learn the sage arts*, one must have an enormous chakra amount, and especially, the guts to never give up. He himself said this is why only naruto and jiraya are and were able to learn the sage arts. Precise chakra control isn't important, if one has enough motivation and naruto proved this - as already told so many times, naruto is dumb (not for me, but this is the way kishi describes him), and moreover, it was never mentioned that he had a precise chakra control. On the contrary, he lacks of it. The only thing that is really important, are the guts to never give up. And as jiraya said, naruto was his only student that had them.
That's why there is no way hinata or anyone else could learn the sage arts. Precise chakra control wouldn't help her much.