Unfortunately it just depends. I feel comfortable giving my nut allergic child stuff that was processed in a facility with peanuts but I do avoid warnings that state that the product was made on the same equipment as peanuts and further avoid "may contain traces of peanuts or tree nuts." Other parents of nut allergic kids also avoid facility warnings, relying on some study that indicated that product with facility warnings has equal or more nut containing product than equipment warning labelled product.
If you want to have treats for this person, may I suggest a company called Enjoy Life? They make snack bars and cookies and are perfect for kids allergic to gluten, soy, eggs and nuts.
I have seen tons of parents bring an allergic child his or her own cupcake too.
DS1 - 7
DS2 - 5
DS3 - 5
Rescue Rott - 3