I know both matters but where do we draw the line to determine which is the greater FACTOR? Actually, "nature" (being so-called "gifted" or "prodigy") is something more debatable than "nurture" since the latter can apply to anyone.
Personally, I consider "nature" for those who started (formally) piano at a VERY young age (say below 5) - especially those who learned to read notes before alphabets. Studies have shown that children learn best during this period (about 4-7 years old). Of course, this does NOT mean everything would be easy for them when they grow up; they still EXERT effort but, having an early age foundation, such effort is not really a "struggle" and is just as natural, usual, and ordinary for them. They to experience difficulty but they solve it faster.
On the other hand, "nurture" is more for those who learned the piano late already (say teenagehood). I just don't know any famous pianist who began piano at 18 or 20.
Sorry if I seemed to be bias on the former. I myself began not that early (9) and I regret not having started earlier. In a sense, I consider myself "self-taught." I do have a teacher but teaching is not only technical. For instance, I don't hail from a family of musicians so I must learn to discipline and encourage myself. And speaking of family, I consider this a BIG factor for I believe it is only the PARENTS who can best encourage (or even force) their children to play the piano at a very young age where normally they would just play around as common kids do. Also, you'll notice most great and famous pianists are foremostly trained by their parents.
These views are just a humble opinion. Please feel free to share yours.