There was a hospital there before the one referred to was built.
McCain's mother maintains he was born on the naval station. So does the English Language Panamanian American, of August 31, 1936, which stated that "Lt. and Mrs. John S. McCain Jr. of the Submarine Base, are the parents of a son born Saturday afternoon at the Submarine Base hospital".
Further a reporter for the Washington Post, Michael Dobbs, says he was shown McCain's birth certificate and it shows his birth as being at the Coco Solo "family hospital."
He checked out the name of the doctor shown on the BC, and found that doctor was assigned to the Coco Solo hospital at that time, thus also showing that there *was* a hospital on the base then, just not the one authorized in 1941. I'll try to find the document showing that assignment. But right now, gotta go, or I'll get no supper.
Found it. Again from the Washington Post's Dobbs
The birth certificate was signed by Captain W. L. Irvine. I have now checked that name against the Naval Register for 1936, and I find that William Lorne Irvine was director of the medical facility at the submarine base hospital in Coco Solo, Panama Canal Zone, during that time period. You can see the entry here.
It's a pdf file or I'd post the image. This provides support to McCain being born on the base, and proves that there was at least a doctor on the base in 1936.
But not having been born in Colon Panama, but rather on the US Navy base, may or may not be enough. He'd certainly have a better shot than someone born with a foreign citizen father. And way more than someone born overseas with a foreign citizen father, or to an unwed mother.