They do think she has ASD, or one of the related conditions.
If they had found 'nothing wrong' they would have told you there and then.
But, it's good news. She's the same person she always was, but now she can access help if she wants it
She can also ignore the label if she wants to. Nobody will never know about her dx unless you told them. You never have to tell anyone really. You certainly don't have to tell university or employers - unless you want to.
But, it allows her to find out more about her quirks, research them, and get support for them. For example she can join an online forum like this for support (She might like www.wrongplanet.net/)
Your behaviour doesn't have to change. School's behaviour doesn't have to change. But your brilliant DD can now ask for help as and when she needs it....
Nothing will change at school unless you go in there and make a big fuss, and seeing as you don't want to do that, nothing will happen or change.
Big hugs. You're doing all the right things. Now you just have to go through the natural grieving process that we too have all been through......