So who can possibly judge whether the appeal school is better when it’s nothing to do with education?
That is the job of the appeal panel. It is precisely what they are there for.
Panels can also take advice. It’s not outsourcing
Appeal panels cannot take advice from anyone other than the clerk, and the clerk can only advise them on the law around admissions and the relevant codes. They must decide the case on the evidence presented. Saying that the social/medical panel decided against you so we aren't going to look at your case is outsourcing their decision and is not allowed.
Where is if documented that the decision was not taken by the panel? That’s entirely spurious
We don't have the exact wording, but OP suggests the decision letter references the decision taken by the social/medical panel. If they simply noted that the social/medical panel came to the same decision, that is fine. If they said that they weren't going to do anything because the social/medical panel decided against OP and therefore the correct process was followed, that is wrong. They should have taken an independent look at OP's case. They could legitimately decide that the social/medical panel got it wrong, or that the social/medical panel were right but they still think OP's child should be admitted. What they cannot do is say that the social/medical panel decided against you so that is the end of the matter.
She can use public info
So you haven't even digested OP's posts properly. The appeal panel refused to allow her to use information that is publicly available, arguing that it was sensitive information she should not have had.