I think that JKR frequently chose to emphasize that it was the choices you made rather than anything else that made you who you were. This is most prominently embodied in the Sorting Hat, of course.

But look at the characters who didn't exactly grow up in the best of environments. Voldemort and Snape succumbed to their darker desires... but then you have characters like Harry and Sirius (and Regulus, if a bit later in life) who made choices that led their paths away from where their upbringing might have led them.