Can we assume that this is the semi-official version on Rowling's
site, and not a quiz a teenager slapped together in 10 minutes somewhere else? Even so, it's useful to point out that a short quiz doesn't reveal much about a person's whole personality, which is why the founders of Hogwarts solved that problem through magic instead.
Cedric Diggory was a Hufflepuff, and very courageous. He did face a dragon, after all. He would have done well in Gryffindor.
On the flip side, Ron Weasley was a scaredy-cat so often (spiders, Quidditch team, etc.), but the Sorting Hat did note that he had hidden courage that would come out when it mattered most. He wasn't a realistic choice for Ravenclaw (indifferent student) or Hufflepuff (too many fights with friends), but he had plenty of ambition for Slytherin. But... a Weasley in Slytherin?? Well, maybe Percy.
And then there was Harry. We know all about that one.
Hermione was an intense child who would have stood out in ANY house... she was highly ambitious, a fierce friend and tireless worker, a voracious consumer of knowledge, and of course, fearless.
So:
1) Just because you were chosen by the Hat for a particular house, doesn't mean you wouldn't do just as well in another house. Except in limited cases (Malfoy), people are complex.
2) You still get to choose. So if he's invested in being a Gryffindor, and he shows the qualities of Gryffindor, he can be a Gryffindor.
