It's true that the parents who actually raise you are your real Mom and Dad, but the word "parent" simply means "a father or a mother...an ancestor, precursor, or progenitor," and when one is writing a story like this one has to use the terms "birth parent," "adoptive parent" or some variation thereof to avoid confusing the reader.
Well, I'll go along with you on the adoptive parents thing just this once because of the cook 9/11 Pentagon story you found on another thread. K? :)