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At the time of adjudication, this kid was and still is a U.S. Citizen but his parents filed the N-600 slightly before they got sworn-in as naturalized citizens. Some parents get confused and file the kids' N-600s at the same time that they file their own N-400s. It is a common misconception that this is the way to do it. There is always the possibility that USCIS will get to the N-600 BEFORE they get to the N-400s AND then at least one parent has to be approved and sworn-in for the kid to "automatically acquire" (derive) citizenship.
The director in Santa Ana, CA relied on what I have condemned as a badly written regulation. AAO seems to have gotten the hint that if they dismissed the appeal and allowed this travesty to find its way into a courtroom that it would be a resounding finding of the decision being, inter alia, "arbitrary, capricious, an abuse of discretion, or otherwise not in accordance with applicable law".
The standard under the INA is a factual finding "to the satisfaction of" the deciding official, which means "at time of adjudication" rather than "at time of filing"--just like for the final decision regarding adjustment of status.