Yes but that's not the full story... .It's true that the odds of dying from anaphylaxis are low, IF treated in time.
The sad thing is that the vast majority of all deaths from allergic reactions are preventable.
Things like not acting immediately and injecting Epipen in the first few minutes, not following up with a 2nd shot if no improvement in 15min. Having expired pens. Kids grow, and need larger pens. Teacher panics and uses pen upside down. Kids try foods as a teen or when they leave home as they "used to be allergic"
As the parent of an Parent of anaphylactic 7 year old - the fear is real. Low odds, but catastrophic outcome.
We are lucky that my partner is a nurse and we are knowledgable and manage places we go, but daycare, schools, birthday situations etc are a worry
*edited - typo