Michael Jordan was born with an insane amount of natural talent and then he worked his butt off to become the greatest basketball player in the world. I was born with a marginal amount of basketball talent and can work my butt off to be the best in my world... the rec center, pick up games, whatever.
The same is true of leadership. Some people are born with a surplus of leadership ability and some are not. We can all work to be the best leaders we can be in our world... at home, at work, at our non-profit, wherever.
I get tired of the nurture vs. nature argument. The answer is yes. Plus it doesn't matter. Plus you should just do the best you can with what you have and not worry about it and stop asking silly questions.