Well, there you have it! Congratulations!
You're eligible if you're over 35 and have moved back at least 14 years. BTW, the reason is your parentage, not the US installation fact.
Of course, a lot of birfers would disagree ... but that leads to absurd results, such as US military should be penalized for serving abroad by having their progeny ruled ineligible to be president.
Well, your answer was much civilized than my questions to you. I apologize for being so harsh. That said, your original post stated that citizens are either Natural Born or Naturalized. That is not the case. I'm both. And to make it even more confusing, I could renounce American citizenship and apply in Germany as a German citizen. As far as I know the US allows only one other nation to have citizenship in both countries at the same time. That would be Israel.