As an EMT who worked in the ER and did triage as a basic, this is likely to happen more often.
It is called TRIAGE for a reason, you assess how the patient is at the time they enter, and move them to a room in the order of priority thus using field skills the same TRIAGE.
I used to second guess my skills and ask my nurse to go see a patient, I think that it is more likely that EMT's and other non nurses will be doing triage in the future as the nursing shortages get worse and as more people keep using ER's as a doctors office.
I doubt that anything could have been done to save this child, as stated, the doctor 2 days prior goofed, but that is what General practice and pediatricians do, they goof a few days earlier then the child comes to the ER, the ER doctor calls the GP or Pediatrician, who says yeah go ahead and send them to the Children's Hospital let them deal with it. Doctors cannot deal with their own patients, so they are rushing through them to get dough and keep hours short.
I heard the other day on the news if you paid like $3500/year in Florida, you got a doctor who had cut their patient list, and you were a VIP, you got the doctors cell phone number and home phone number to call for issues, you got to sit down and tell your doctor about your problems instead of the in and out trip we all are accustomed to.. This system is only going downhill.
I think a paramedic or any EMS provider should be adequate at TRIAGE, and think it is great training for what could happen in the field.... Too many patients and not enough providers.