I’d say that any injury that requires a trip to the ER requires a call to a parent.
What if the kid had an allergy to a particular med? What if the family was Jehovah’s Witness and a blood transfusion was contemplated, etc. There are a number of reasons why the parent should have been called, even if the finger tip was reattached. Shoot, I’d need the docs to tell me how to care for a reattached fingertip.
But that’s just the lawyer in me. It’s not that you have to sue, but people need to be called out on their stupid behavior. The next time, a kid could wind up dead or needlessly sickened.
I would say that any out of the ordinary requires a call to a parent.