You do realize these kids were tested first to see if they had a peanut allergy.
FTA: "All had been given skin-prick tests to make sure they were not already allergic to peanuts. "
So they took precautions to make sure they kids weren't already allergic, something a parent isn't going to know. If you kids are allergic to eggs or had eczema, they might be at risk to having an allergy to peanuts. So the first thing you don't do is shove peanuts down their throats! You'd better have your child tested first. IF, they don't have an allergy, THEN you can give them peanuts, which should help prevent them from developing one.
Which is interesting because the allergists I've talked to don't seem to think the pin prick test for peanuts is conclusive. Apparently since this headline isn't "Children drop dead after being told to eat peanuts 'For Science'" that it is a decent way to test for it.