She is correct, schools cannot diagnose.
They can only find him eligible/ineligible in the 13 categories. One is autism, one is IDD. I'm assuming, perhaps incorrectly, with trisomy 21 that he's currently eligible under IDD.
Category shouldn't drive supports and services but it often does. It also shouldn't drive placement, but often does.
Ideally, the newly identified needs will be found thru these assessments, and then a better IEP can be drawn up.
She can say "we don't find him eligible for the autism category" based on the evals. Fine, then he's a kid with Trisomy 21 who also has sensory needs, pragmatic language issues...whatever else. Just make sure the actual needs are identified.