Actually McCain was born at the base hospital. His mother wrote about the experience. Sorry that I don’t have a link to it.
According to the birth certificate and COLB of John McCain, McCain was born in Colon Hospital, city of Colon, Panama. While the BC states at the top that it is from the Canal Zone, the document also states that McCain was born in Colon Hospital, city of Colon. The city of Colon and the hospital were not in the Canal Zone.
The common story you hear is that McCain was born in the Canal Zone, but these documents posted online do not testify to that. Furthermore, there is no official document that has ever surfaced which states that McCain was born in the Canal Zone.