If, and only if, you limit the scope of the logic to CSAM, which is my point.
The logic, by itself, could apply to any video evidence of crime. For instance, if we want CCTV videos to remain admissable in court, then according to parents logic, we need to outlaw any video generation of CCTV format, otherwise every defendant can simply claim the videos are fake.
But it is a lot easier to have folks who are in charge of systems testify as to their authenticity than to have a child who has been abused testify to the authenticity of the abuse, thus the logic is defensibly limited to child abuse.
Exactly my point? We don't need to come up with a generic legal basis or reason, we can just say "CSAM is special" in a legal sense.
When you introduce a picture or video in a trial (or hearing) then someone with knowledge of the video must appear to "lay a foundation" and say what is presented is true and accurate and genuine. Often there are stipulations to avoid this (e.g. in a murder trial it generally pisses the court staff off if the defendant demands that the crime scene photographer turns up to say they took the photos of the body), but it is still not uncommon for a lab technician to be brough to court to explain how they processed some drug sample.
The poster a bit above you was right about the problem with AI. If we say AI CSAM should be legal then we might end up with the scenario that all CSAM is considered fake unless we can uncover the victim or perpetrator and have them brought to court to say they took the photo or video. It's a very tough legal problem.