Doctors make deadly mistakes every day. EVERY DAY. They are far from infallible. So unless he had actual proof such as lab results or symptoms that pointed to something like meningitis or appendicitis or flu the parent’s rights do not come secondary.
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.