I had a friend who gave birth to her son while in Cyprus with her husband. Her story was that whilst in labour the ambulance had to rush her to the hospital from her MQ because if the son had been born closer to the MQ site the son would be classed as Turkish and eligible for Turkish military service.
As for my memsahib, she was born one of the Naval hospitals in Malta while her dad was posted out there. Listing her place of birth has caused questions over the years, so when it came to renew passports she applied for a replacement birth certificate in case her original got lost in the post.. The UK side of things had real problems finding the details, several emails were sent in both directions and eventually they found the right book and the right page and managed to issue a replacement.
The Maltese office returned the correct document within two weeks.