My younger sister and I were adopted by my step-father when I was 14 and we had to go in front of a judge in a courthouse conference room. My mom's lawyer was there and the papers were filed at the courthouse then copies were sent from Florida (where we were living) to New Jersey (where we were born) and our birth certificates were changed.
If the goal is to find records, maybe they have a contact in the courthouse...a clerk or someone, who can look it up for them.
Hope this helps...