This is just wrong. He entered the country legally. The Adoption Citizenship Act seems like the right way to handle this.
The reason the law was that way is to prevent loopholes like someone adopting a 30 year old person and then using this law to naturalize them.
Usually though good faith and bureaucracy don't mix. It is dangerous to have faith in bureaucracy. In a way that is what the parents did, how the girl at the end said her parent just believed common sense would prevail and even if there is a missing paper here and there, someone sitting across the desk will understand and fix the error eventually.