Sure, you need to know what to look for, and that's a fair criticism, if they weren't told. But from your description, the child was very bad. I have seen some children given some pretty dangerous things in that type of situation because there was no choice.
You are correct -- sometimes there is absolutely no choice because there isn't time. Learned a long time ago when my children were small to have their doctor's on staff at children's hospitals if possible. My kids were fortunate in that we lived in areas that had children's hospitals except in NH/MA where we were not close to any. The difference was a shock.
My youngest daughter had a reaction to a sulfa derivitive when we lived in CA -- she had been given it when she had a bad ear infection and her records stated that she was not to be given any sulfa related drugs. Got to MA, she had an ear infection, and when I took the prescription to the pharmacy, I asked them if this drug was sulfa related -- sure enough it was so I went back to the doctor who said it wouldn't bother her. He had never even bothered to check a copy of the records I had handcarried with me in case of an emergency. That taught me a valuable lesson -- ask questions!