My daughter was also born at Rinteln while I was getting some winter sun early in 1991 - green walled room, no pool or aircon.......
She has a birth certificate issued by HQ BAOR - signed off by a Maj Frank Crabtree. Looks fairly official to me and worked fine for getting passports etc
Ditto for my son, who was also born at Rinteln, in the early 1980s. The name Major Crabtree rings a bell, too.