That was because McCain was known to have technically been born outside of the US. He was born in Panama, although not in the base hospital, but had been registered as a US birth because his birth in the non-military hospital was due to some fluke (no OB department in the military hospital at that particular moment, IIRC). Therefore it was important to assert that both his parents were US born and his father was serving military.
I fell for that claim until someone pointed out the evidence that it was false. McCain was indeed born outside the United States proper, but he was not born outside of a United States Military Hospital as has been alleged all over the internet. There is a fake birth certificate floating around on the net showing him as being born in a Panamanian Hospital, but this document was fabricated. His real birth certificate is not available online because he has not released it. He has shown it to a few people, but that is all.
You are mistaken. McCain was born in a clinic on the base, the forged birth certificate proporting to show his birth in Colon notwithstanding.