RSBM
As Natalia spent her early years in a Ukrainian orphanage, presumably in a ward for children with disabilities, it is quite possible she had very little exposure even to her native language before leaving the orphanage, as the children are paid so little attention by staff and are left on their own in their cribs without stimulation or human contact much of the time. If that is the case, English may for all intents and purposes be her "first language" – at least, the first she was exposed to regularly enough to absorb the basics of verbal communication, in the time she spent in her first two adoptive homes and wherever she was in between those two adoptions. (Foster care? A US orphanage? Do we have any idea?) Therefore her pace of learning English may have been closer to that of a baby/toddler's rapid acquisition of language in the first two years (roughly; as parents know it varies child to child) than that of an older preschooler or elementary-age child beginning to learn a second language after developing his/her early communication skills in another. If Natalia is not cognitively impaired, but simply delayed due to an early childhood of profound neglect and inattention, this could be an explanation for her fluent, unaccented English by the time the Barnetts encountered her – after she left Ukraine she was exposed to a variety of people trying to communicate with her in English for many months, after years of isolation from meaningful language. She was a tabula rasa, and she sucked it up like a sponge, just like babies do.
MOO, IMO, etc. I am not a language development expert!