You are right just as John McCain and Barack Obama Marco Rubio are not natural born citizens. According to Vattel Chap 19 in the law of nations, which the founders based the constitution.
The natives, or natural-born citizens, are those born in the country, of parents who are citizens. As the society cannot exist and perpetuate itself otherwise than by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights.
The Canal Zone at the time was not a possession or territory of the United States so McCain was not eligible to be POTUS either.
What I find really interesting is that McCain, Obama, and Rubio all show up within a very narrow window of time and express interest in the presidency. It's almost like the issue is being overloaded so that everyone finds it boring and just wants to ignore it. Neither party is likely to press the issue because both parties have big names with life histories that might at least cause people to ask questions.
It's almost like a set-up to make Obama's origins seem insignificant.