It’s not just a technicality.
Otherwise you end up in the subjective realm of... ok , how long can a kid live overseas before having ties to the soil he was born on? What majority of a persona early life has to be lived in a given area before becoming bonded to that area. It is far easier to make the distinction at birth and have it stand. Citizenship is decided at BIRTH legally. No other time. That is the instant where it is decided, and that technicality matters.
Also, your daughter, unless she was born on a US Military base, would not be a Natural Born Citizen. A citizen yes, but Natural Born, I am afraid not. I am not pointing this out to make you wrong or to in any denigrate you or your daughter. In order for her to have definitive US Citizenship status at the laws of the time she was born, likely you did have to do all that to secure her US passport and any other documents you needed at the time. I don’t know when she was born, so I can’t say specifically.
What I have been researching are the laws at the time of Obama’s birth. Which at that time, would mean that both he, and your daughter (if she were born in 61) mean that they are not Natural Born Citizens. You must have two parents who are citizens and be born on the soil of the country or its territory.
Doesn't matter if the birth was on a base or not. What matters is that the parent(s) were outside the country but in its service. If they were, and both are citizens, the child is still natural born. See Vattel, book 1, section 212 and 217.