It is Dosey's life, and yes she can refer to her parents (both sets) in whichever way she wishes. However, I don't agree that Ecclefechan is "getting hung up on terminology".
It is generally accepted within the adoption community that there are certain terms which are unacceptable (and to be honest insulting) to the various members of the adoption triangle.
Real parents - normally used to refer to the biological parents of the child. The flip side of this is that it implies that the adoptive parents are in some way unreal/made up/fake/pretend. Therefore it is quite easy to see why Ecclefechan's DD is upset by people using this term.
Natural parents - again normally used to refer to biological parents, with the implication that the adoptive parents are unnatural.
When referring to the biological parents it is normal for them to be called birth parents (birth mum, birth dad, birth siblings etc.), and the adoptive parents as adoptive parents when needing to differentiate, or just parents the rest of the time.
If you read the links in the posts above, you'll see that often the 'real' parent issue is high up on the list of things that are unacceptable to say to adoptive parents.
Sorry to derail the thread, but I think it's important that people are aware of what the appropriate terms for people are.