Actually, he is eligible. The USPHS uses military ranks, but they’re not actually in the military and they need not have been in the military. I have a buddy whose wife was a Captain (Navy type, O-6) in the USPHS and she never served in the military. The Surgeon General is a presidentially-appointed position like Secretary of the Navy, who need not have served in the Navy (unfortunately).
There are Surgeon Generals though of the Air Force, Army and Navy
Surgeon General of the United States Air Force