Why would all passengers be asked not to eat peanuts when there is one allergic person on board?
The problem with a severe peanut allergy is that you don't have to eat a peanut to be affected.  With a severe enough allergy, inhaling peanut "dust" can trigger a life-threatening emergency.  In a confined space, any number of events could cause an issue: people dumping peanuts into their hands, dusting their hands off, accidentally sneezing while chewing the peanuts, etc.