That might or might not matter. Sometimes it is the residence of the parents that matters, not where the delivery occurred.
It's also not entirely clear that he was born in a civilian hospital off base. Back in the late 1930s, home births were much more common, I think my parents were each born at home. It was at least 30 miles to the nearest hospital for my maternal grandmother, and I don't know exactly where my paternal grandparents were living when my father was born, except that his BC shows "Choteau Montana". My father in law was born in a hospital, but he was also Cesarean and subsequently an only child, much to the chagrin of his mother, who was nonetheless quite thankful to have him, and she did end up with 5 grandchildren, and many great grandchildren, a few which she actually knew before she got too senile to know anyone.
Pretty sure my mother in law was a home birth too, and she isn't that much older than McCain. Let's see, she turned twelve on 7 Dec. 1941, (an easy date to remember, and my daughter's is the next day) so she was born in 1929 to McCain's 1936.
I was startled to find that while the hospital I was born in, in 1949, was established in 1889, making it the oldest hospital in the city, and the physical building was more or less as it was in '49 by the early '30s. (And is today, but it's not a hospital any longer, that's now across town) they didn't start delievering there babies until 1942.
Also there could have been some kind of medical facility that was less than a full hospital on base. The docs, or nurses, on the base may have made housecalls, especially for the wife of an officer whose father was already quite high ranking by the standards of the interwar Navy.
But still within the Canal zone to US Citizen parents, I believe. And by the 1904 law, that still makes him a citizen at birth, if that is the same as being a natural born citizen.
But be that as it may, the supposition that he was born off base is driven by the construction date of the on base hospital. But as I pointed out earlier, not all babies, or even most babies, were born in hospitals in 1936.