I suspect his persistent confidence was already there to lead him to write to Disney in the first place. As a kid, I had an idea like that and my Dad was going to write to the company but he never did, I never had the inclination to do it myself, and now I'm not an actor.
It also takes some awareness to state your age at the start of the letter. That's what makes people respond so well to it. I would never have thought age was relevant, or even that it was shameful to admit you're just a child. I didn't understand how people think. This guy apparently did, so again, he was already cut out for acting, I'd say.
Good insight. Yes, I do remember at the time, purposely thinking I must lead with my age knowing instinctively that somehow that would help me and they would be more likely to pay attention.