You’re right, doctors make mistakes. But if the toddler was taken to the ER unnecessarily, what are the likely consequences versus if a critically ill toddler were not taken to the ER? Every decision in medicine is a risk equation, and so is police work.
We don't know, and who are you to decide for the family.
Remember the mother only decided not to take the child to the ER when the fever had broken and the child was active. So critically ill did not arise.
Now here is another consideration. Why didn’t the doctor call for an ambulance if she believed the child could have an extremely serious communicable disease? She certainly would have been justified in doing so if meningitis was feared. How worried could she have been if did not take steps to make 100% sure the child was examined by an ER doc and tests run?