A few thoughts
First, I do think it is very important to remember you are talking about little kids. Kids are not always thoughtful about what they are doing, don't always pay attention even if they are told something serious, and often do not consider the consequences of their actions.
You have to realize, with very severe nut allergies, kids can have reactions from just TOUCHING a surface that has been touched with peanuts, and even in some cases from inhaling peanut particles. I don't know if this girl was this bad off, but given that, and the severity of the possible reactions, it simply does not pay to take ANY sort of chance.
As a teacher, I look at it simply like this;
The pros of "no nut snacks" is there is little to no chance of this kid dying in class.
The con is that other kids don't get to eat a nut during snack at school that year.
Personally, there is no other thing to consider there.
About the girls panic attack... honestly, I DO kind of understand. As I said, she is a little kid, and if she knows that roughly two or three feet away from her is something that can kill her, something that she knows to be ESPECIALLY aware of, something she has probably been told MANY times will kill her if she eats it (you have got to make it serious so a kid won't sneak a taste, hoping that "Mom or Dad aren't looking" because they don't quite get it) I think that it actually can be understood. The girl actually excused herself to go to the nurse before falling apart, so I suppose she did sort of restrain herself, but still, no child in a classroom should have to deal with that.
As for using it as a learning experience, I do understand where that comes from, since she will likely be faced with nuts in her life, but again... she is a little kid. The people around her are little kids. There is no parent around. If she is going to learn "life lessons" about peanuts, snack time at school is probably not the time for it.
And Indoor, in a school among children away from their parents and their homes it is very much about group responsibility, and group safety. I firmly believe that, and I have a feeling in this sort of case you probably do too.
And yeah, the main point of the story is the totally inappropriate, selfish reaction of the one father and one mother. It baffles me that any parent with any amount of empathy or understanding would EVER do that.