“should be allowed to go through the Naturalization process without the wait.”
So, you are saying that she is a a Dreamer?
No. A “dreamer” is someone who came or was brought here illegally or was born here to an illegal mother.
The lady in question was brought here by an American Citizen legally and, it appears, adopted legally. Having gone through the process, it’s likely she was issued a new birth certificate in her new name (given to her by her adoptive parents) after a private adoption in front of a judge (an assumption), which allowed her to obtain a social security card.
The fact that her parents didn’t know (an assumption) that the adoption didn’t make her a US Citizen should not be held against her. She should be allowed to go through the Naturalization process.
Dreamers’ whole existence in the US is illegal. If they want to go back to their home country and go through the legal immigration and naturalization process, I don’t think anyone would have a problem with that. If the US wants to waive waiting times for this, I don’t think anyone would have a problem with that, either.