One kid eats a peanut butter sandwich. Being a kid, some residue remains on his hands. He touches a chair. The peanut oil is on the chair. The allergic child touches the same chair and then touches his mouth.
That's enough. My wife has seen a teen who went into a coma from eating brownies. They had no nuts in them, but the pan had been used before to make peanut butter cookies and and when it was washed not all of the peanut oil got removed.
SD
If that is truly the case then the child does not belong in public school.
So, using your previous example with the chair: a kid eats a brownie baked in a pan previously used to make peanut butter cookies, being a kid residue remains on his hands and he touches a chair, when the allergic kid touches the chair.... Therefore, prohibiting peanut butter from the kindy class is useless. This child, if indeed that violently allergic needs to be homeschooled -- or, perhaps we should just make it illegal for children who attend the same class as this child to have peanut butter in their homes.
And, yes, I do doubt the mother. I've had to deal with mothers like this before and without exception they've been trouble. A friend of mine has a child who is severly allergic to peanut butter and she doesn't play these games. She makes the necessary adjustments and finds a way to live in this world without expecting the world to change for her.