I don't believe there is any "born with it". Certainly there are some congenital chemical differences in our brains but the heart of a fighter is something that we get from our upbringing and experiences. I think there is a point in our development where that heart cannot be learned any longer, we are essentially set to the person we will be deep inside. And no amount of training can turn someone who hasn't got that heart into a champion once that period has passed.
And I don't think it has anything to do with streetfighting, streetfighting isn't any sort of great training tool, most streetfights involve ridiculous odds (been there a time or two myself) and aren't about heart, they are about brutality and meanness. Streetfighting just teaches someone how to hurt someone else with the cheapest methods possible, it doesn't give you the heart to win a referree'd one on one battle with an equally or even greater-skilled opponent.
Objection, Your Honor. He's reciting the opening to Quantum Leap.