I think it is a lot more down to innate ability than people like to admit. That's not to say that lack of support and difficult circumstances don't limit students with a lot of inate ability, though.
But:
-If you find it easy to sit and concentrate, you are naturally praised for this and receive a lot of positive reinforcement from an early age.
-If you find school generally easy, then you will likely enjoy it more, and develop a love for learning.
-If you do well on assessments, you will receive a lot of praise and so assessments don't become such a daunting, scary thing.
-Because you're getting all this positive reinforcement, and you don't find studying difficult, you're more willing to study, and it becomes a virtuous circle. This might be supported by tutors/parents etc, but the student will enjoy engaging with them.
-Because you see yourself as "clever", you don't find difficult things so daunting- you know you normally grasp them, so you're willing to put the work in.
This sort of child, given access to good schools and with good support will usually do well and achieve pretty high exam results.
Equally, if as a young child, you find it harder to sit and concentrate, and you have some early negative results- it's much more likely you will switch off from education, or not have such an interest in it. Therefore, engaging with a tutor will feel more like a chore or a punishment, and you may not see such immediate results.
The right kind of teaching will obviously make a difference to this sort of student, but real hot housing will make them miserable.
So I do think innate early intelligence, good concentration, and personality all have an impact, regardless of the opportunities given.